That's OK.
Leaving the post up might help others with similar problems.

Question #1

That's great! Thank you for letting me know.

Question #2

Unfortunately, Juicebox has no way to split an image into individual hit areas and associate each one with a unique link.
The easiest way to include two different links into a specific image would be to use an image caption such as this:

<caption><![CDATA[Click <a href="http://www.example.com">here</a> for Link #1.<br>Click <a href="http://www.example.com">here</a> for Link #2.]]></caption>

If you are entering the caption directly into the JuiceboxBuilder-Pro interface, then you can use just something like the following

Click <a href="http://www.example.com">here</a> for Link #1.<br>Click <a href="http://www.example.com">here</a> for Link #2.

... JuiceboxBuilder-Pro automatically adds the <caption> and CDATA tags to the gallery's 'config.xml' file.

You can further style the caption/link text with inline CSS if you like, as noted in the FAQ I linked to in my last post (here).

If you don't want the caption area to be seen on other images in the gallery, set showImageNumber="FALSE" in the Caption section (to hide the image number in the caption area) and set the opacity for both captionBackColor and captionBackTopColor to zero in the Color section (to hide the caption area gradient).

I hope this helps.

You can prevent the thumbnails from being displayed when the gallery is loaded by setting:
showThumbsOnLoad="FALSE" - (for Large Screen Mode) - Thumbnail Options
showSmallThumbsOnLoad="FALSE" - (for Small Screen Mode) - Thumbnail Options

You can prevent the user from toggling the thumbnails on and off (by disabling the Thumbnail Button on the Button Bar) by setting:
showThumbsButton="FALSE" - (for Large Screen Mode) - Lite Options
showSmallThumbsButton="FALSE" - (for Small Screen Mode) - Thumbnail Options

Juicebox was not designed to default to fullscreen mode and requires a click from the user (on the Expand Button on the Button Bar) to go into fullscreen mode.
If you really want your gallery to go fullscreen as soon as the gallery is loaded, then you could try one of the following suggestions but please remember that Juicebox was not designed with this in mind so you might encounter some unexpected problems.

(1) If you link directly to a web page containing a gallery, then try adding #expanded to the end of the URL.
As an example, take a look at this embedded demo gallery: https://www.juicebox.net/demos/pro/embedded/
... and now go to the same URL but with #expanded at the end of it: https://www.juicebox.net/demos/pro/embedded/#expanded

(2) If you cannot use a URL to automatically expand your gallery, then you could perhaps use the Juicebox-Pro API method toggleExpand() (within the onInitComplete event) inside your gallery's embedding code to fire fullscreen mode when the gallery is ready.
Here is some sample code which you could use to achieve this.

<!--START JUICEBOX EMBED-->
<script src="jbcore/juicebox.js"></script>
<script>
    var jb = new juicebox({
        containerId: "juicebox-container",
        galleryWidth: "600",
        galleryHeight: "400",
        showExpandButton: "TRUE"
    });
    jb.onInitComplete = function() {
        jb.toggleExpand();
    };
</script>
<div id="juicebox-container"></div>
<!--END JUICEBOX EMBED-->

I hope this helps.

Edit:
Please note that if your gallery sets useFullscreenExpand="TRUE" (Lite Options) then neither of the suggestions above will trigger the Fullscreen API to go true fullscreen. (The gallery will expand only to fill the browser window, not the entire screen.)
This is due to a security feature of the Fullscreen API (please see here for further details) whereby the user must initiate the true fullscreen functionality via a click (on the Expand Gallery Button on the Button Bar).

I'm glad to hear that you've been able to resolve your problem.
Thank you for letting me know (and for sharing the link).

By default, the Download Button will download the image being displayed in the gallery (using the imageURL from the gallery's 'config.xml' file, the same path that Juicebox uses to display the image in the gallery).

If you have a Multi-Size Image gallery, then the Download Button will download the 'large' size image (the largeImageURL) in preference to the imageURL.

If an image has a linkURL associated with in, then the Download Button will download the file pointed to by the linkURL in preference to all of the above.

Please take a look at your gallery's XML data to check the imageURL, largeImageURL and linkURL entries to see if you can figure out where the problem is originating from.

If you are using the Juicebox module for Drupal, then please note that this is an unofficial plugin which was not written by ourselves.
The gallery's XML data is dynamically generated by the module's code and so, if you are unable to determine the cause of the problem, then it might be worth posting your query in the Drupal forum where the author of the module might be able to help you further.

Also, it might help if I am able to see the problem for myself so if you continue to experience difficulties, please post back with the URL to your gallery's web page so that I can take a look and hopefully help further.
Thank you.

Edit:
As your Download Button seems to be downloading the 'juicebox.php' file (but with an .html file extension), it might be worthwhile checking that PHP is installed and configured correctly on your web server.
The Download Button requires PHP 5.2.0 or later, as noted here (check the 'Web Server' system requirements).

The custom CSS is affecting the position of the image within the Splash Page container and the only way to counteract this is with CSS. The custom CSS will be applied to whatever image you choose to use for the Splash Page, no matter what shape or size it is.
Additionally, if your gallery is responsive, then the aspect ratio of the Splash Page will be dependent on the dimensions of the browser viewport being used to view the gallery so you have no way of knowing what shape and size the Splash Page will actually be for any given user (so there is no ideal size to use for the Splash Page image).

The quickest and easiest solution to the problem is to ensure that the max-width: 100% !important; CSS rule is not applied to the Splash Page image by removing the !important declaration from the rule. (This will likely not adversely affect other images on your web page at all.)

However, if you do not want to change the Jetpack CSS, then you'll need to change the Juicebox CSS instead.
Open the plugin's 'wp-juicebox/jbcore/classic/theme.css' file in a plain text editor.
Search for max-width: none; and replace all instances (there are four) to max-width: none !important.
In the current version of Juicebox-Pro (v1.5.1), they are on lines 119, 197, 247 and 696.

Otherwise, you could just add the following to the end of the 'theme.css' file:

.juicebox-gallery img, .jb-idx-thb-list .jb-idx-thumb img, .jb-dt-main-frame img, .jb-idx-thumbnail-container .jb-splash-holder img {
    max-width: none !important;
}

As the 'theme.css' file is loaded in your web page after the 'style.css' file, the !important declarations in the 'theme.css' file will override the !important declaration in the 'style.css' file

I hope this make sense and helps you to resolve your problem.

You're welcome! I'm glad it worked. Thank you for letting me know.

Please post suggestions for future versions in the Feature Requests forum thread. (You can post suggestions for Juicebox and all official plugins written by ourselves there.)
This keeps all the requests together and ensures that they will not be overlooked by the developers.
I do not know the likelihood of any ideas being implemented in future versions but this is certainly the best place for all ideas.
Thank you!

No. Unfortunately, there is no Juicebox plugin for darktable.
All known plugins for Juicebox are listed here.

The Juicebox plugin for Lightroom requires Lightroom 4, 5, 6, Classic CC 7 or higher.
This is noted on the plugin's own support page here.
(The plugin will not work with Lightroom CC.)

In late 2017, Adobe split what was then known simply as Lightroom CC into two separate products. Lightroom CC became Lightroom Classic CC (currently on version 8.2.1) and Adobe released a new version of Lightroom under the name Lightroom CC (currently on version 2.2.1).
Unfortunately, the new Lightroom CC does not accept third-party plugins or web engines so it is not possible to use the Juicebox plugin with this version.

There are other ways to create Juicebox galleries, though (you do not need to use Lightroom).
You can use JuiceboxBuilder (the standalone desktop program to create and edit galleries) or the Juicebox Photoshop Template (if you have Photoshop) or you can create a Juicebox gallery manually using the sample 'web' gallery as a template following the Manually Creating a Gallery instructions.

I hope this helps to clarify things.

When using JuiceboxBuidler-Pro to create a gallery and resize images, you can set whatever image dimensions you like (in the 'Set Image Sizes' control panel after clicking the 'Change Sizes...' button on the 'Images' tab).
Please note that these image dimensions are maximum image bounds (rather than the actual dimensions for the resized images).
Images are resized respecting their aspect ratios and the resized images will always be within the maximum image bounds.
However, if your source images are square, then the resized images will also be square.

The background will always be the same size as the gallery itself.
The gallery dimensions are set via the galleryWidth and galleryHeight configuration options (in JuiceboxBuilder-Pro's 'Customize -> Lite' section) which are set in the embedding code.
galleryWidth and galleryHeight can be fixed pixel values or percentages.
If using a galleryWidth of 100%, for example, then the gallery's actual width will be 100% of the width of the gallery's parent container (so the gallery's actual width will be dependent on other containers and CSS on the embedding page).

The Juicebox Module for Drupal is an unofficial plugin which was not written by ourselves.
As such, methods of resizing images and setting gallery dimensions will likely be different to how it is done in JuiceboxBuilder-Pro.
If the module's own documentation (found here) does not help, then I'd recommend that you post your query in the Drupal forum where the author of the module (Ryan Jacobs) should be able to help you further.
He is active and very helpful in the Drupal forum and has a much better knowledge that I have of both the module and Drupal itself.

I hope these notes point you in the right direction.

Unfortunately, I'm not exactly sure what you mean.
Maybe you could explain your problem in more detail (let me know what you see and what you expect to see) and, if possible, post screenshots to demonstrate the problem.

In the meantime, maybe my notes below will help.

When using Juicebox-Pro's Background Image Options (found here), you can select the backgroundScale (STRETCH, FILL or NONE) in JuiceboxBuilder-Pro's 'Customize -> Background Image' section but the background image itself does not change (and is not adjusted) which each image within the gallery is viewed.

You can set your gallery's backgroundColor to be transparent (set the Background Color Opacity to '0' in JuiceboxBuilder-Pro's 'Customize -> Lite' section) and whatever CSS background you set in your gallery's embedding web page (whether for the gallery container or the entire web page) will shine through the gallery.
If you wanted to, you could then adjust (or change) the background depending on the image currently being displayed in the gallery (using JavaScript and CSS).

Here is an example which changes the gallery's background color to red for a portrait style image, green for a landscape style image and blue for a perfectly square image. You could modify the JavaScript to alter the background and way you like, for example to completely change or adjust the size of a CSS background image.
To see this example in action, create a sample gallery with JuiceboxBuilder-Pro and use the following as the gallery's 'index.html' file.

<!DOCTYPE html>
<html lang="en">
    <head>
        <meta charset="utf-8" />
        <meta name="viewport" id="jb-viewport" content="width=device-width, initial-scale=1.0, minimum-scale=1.0, maximum-scale=1.0, user-scalable=0" />
        <style type="text/css">
            body {
                margin: 0px;
            }
        </style>
        <script type="text/javascript" src="jbcore/juicebox.js"></script>
        <script type="text/javascript">
            var jb = new juicebox({
                backgroundColor: "rgba(0, 0, 0, 0)",
                containerId: "juicebox-container"
            });
            jb.onImageChange = function(e) {
                var index = e.id;
                var info = jb.getImageInfo(index);
                var url = info.imageURL;
                var img = new Image();
                img.src = url;
                var imageHeight = img.height;
                var imageWidth = img.width;
                var imageRatio = imageHeight/imageWidth;
                if (imageRatio > 1) {
                    // Image is portrait style
                    $('#juicebox-container').css('background-color', '#ff0000');
                }
                if (imageRatio < 1) {
                    // Image is landscape style
                    $('#juicebox-container').css('background-color', '#00ff00');
                }
                if (imageRatio === 1) {
                    // Image is perfectly square
                    $('#juicebox-container').css('background-color', '#0000ff');
                }
            };
        </script>
        <title>Test</title>
    </head>
    <body>
        <div id="juicebox-container"></div>
    </body>
</html>

I hope this help to clarify things and point you in the right direction.
If not, then please explain your problem in greater detail and I'll try to help further.
Thank you.

I see the difference in widths between the id="box_slideshow" and class="jb-splash-background" containers when I view your gallery in a narrow viewport (< 1024px), changing the user agent string in order to view the Splash Page, but I have been unable to replicate the problem in a test scenario of my own.
I embedded several galleries on a test page (gallery vs Splash Page, with and without a CSS margin being applied to the gallery container, with and without a CSS padding being applied to the gallery container) but do not see any discrepancy in the widths of the id="box_slideshow" and class="jb-splash-background" containers.

I can't quite wrap my head around the problem in your web page as you are using custom embedding code and there is a lot of external CSS to look through with many CSS margin rules (and I do not know how many, if any, are relevant to the problem at a glance).

Please take another look at your code (check all your CSS margin and padding values) to see if you can determine the cause of the problem.
I cannot replicate the problem myself in a stripped back example so the cause may lie somewhere within your code (and you'll certainly have a better understanding of your own web page's code that I do).
I can't be sure that your code is at the root of the problem but, being that I have so far been unable to replicate the problem, it might be worth another look.

Maybe its simply a case of the class="jb-splash-background" container not inheriting custom CSS being applied to the id="box_slideshow" container, in which case, whatever custom CSS you apply to the id="box_slideshow" container, you could also apply directly to the class="jb-splash-background" container. Not an ideal solution, perhaps, but it should t least result in matching widths.

The problem could also be due to the way that custom CSS is being applied.
For example, when setting Juicebox's height to a percentage value, it may be necessary to explicitly set the height of its parent divs via inline CSS (as noted here).
It is just a thought but if you are not already doing so, maybe you could try using inline CSS to apply your margin.

I've checked my browser's developer tools but don't see any obvious custom CSS which is causing the problem so maybe the issue is somehow due to custom CSS being applied via JavaScript.
Again, I'm not sure about this at all, but it might be another avenue to investigate further.

I notice that you use setGallerySize(width: int, height: int) within onInitComplete.
Maybe this is the root of the problem and it would help to calculate the width and height of the gallery before the embedding code and then set the galleryWidth and galleryHeight within the embedding code (instead of afterwards via the Juicebox-Pro API methods).

I hope my notes above help to some degree.