It sounds like your gallery might have fixed pixel dimensions (rather than being responsive) and, if so, it will always be displayed at the specified dimensions on all devices and in all browsers.

There are essentially two ways to make a Juicebox gallery responsive (with its dimensions dynamically changing with the size of the user's browser window).

Scenario #1:
A Juicebox gallery will be responsive (and will dynamically scale with the size of the user's browser window) if the gallery's own dimensions and the dimensions of all parent containers are expressed as percentages. If there is a fixed value anywhere up the chain, then the gallery's size will become fixed (e.g. 100% x 100% x 800px = 800px).
Please note that when using percentage heights, you may need to implement the suggestion noted here.

Scenario #2:
You could use JavaScript to listen for a change in the size of the user's browser window and assign new dimensions to the Juicebox gallery if and when this happens.
An example of this can be found in the resizable galleries support section here.
Take a look at the source of this sample gallery in your browser to see how this might be achieved.

Both scenarios above apply equally to Juicebox-Lite and Juicebox-Pro.

You can certainly use WP-Juicebox (the dedicated Juicebox plugin for WordPress) on its own.

WP-Juicebox comes bundled with Juicebox-Lite but if you are a Juicebox-Pro user, you can upgrade the plugin to use your Juicebox-Pro files by following the instructions here.

No. JuiceboxBuilder-Lite (the desktop application to create and edit Juicebox-Lite galleries) is found inside the Juicebox-Lite zip package which can be downloaded from the link on this web page. (JuiceboxBuilder-Pro is found inside the Juicebox-Pro zip package.)
More information about JuiceboxBuilder can be found in the links below.
JuiceboxBuilder Tour: http://www.juicebox.net/tour/juiceboxbuilder/
JuiceboxBuilder User Guide: http://www.juicebox.net/support/juiceboxbuilder/

This is where the problem lies. A Juicebox gallery shortcode should not be copied and pasted into a different page. Each Gallery Id is linked to the page or post that it was originally created in.
If you copy a shortcode, it might initially display the images attached to the original page but if you edit and update the page, then the gallery will become linked to the new page and will then display the images attached to this new page.
As long as you do not copy and paste gallery shortcodes, everything should be OK.
If you want to recreate a gallery for different pages, you will need to re-upload the images for each page. (Wordpress natively allows each Media Library image to be attached to only one page.)
If you do not want to have to upload images to the Media Library multiple times, then you could perhaps use Flickr as a source of images and use the same Flickr options in each gallery.

Make sure that you do not click 'Insert into post'. This will display the images directly in the page. All that is required to display images in a WP-Juicebox gallery is to attach the images to the post. Just close the media window after uploading is complete.

A WP-Juicebox gallery sourced by the Media Library will display all images attached to the post. If you want to use Media Library images in the page but outside your Juicebox gallery, then I would recommend that you either use a different image source (such as Flickr) or create your galleries using JuiceboxBuilder and embed them manually using the baseUrl method of embedding documented here (without using WP-Juicebox at all).
Essentially, once you have created a gallery with JuiceboxBuilder, you would upload the complete gallery folder (not just the contents) to your web server and paste the baseUrl embedding code into the body of your WordPress page (ensuring that the method of entry is 'Text' rather than 'Visual'). It does not matter where on your web server you upload your gallery folder to as long as the two paths in the embedding code (the path to the 'juicebox.js' file and the baseUrl itself, pointing towards the gallery folder) are correct.

Unfortunately, there is currently a known bug whereby the default value of maxThumbRows (1) is not respected on small screen devices when screenMode="LARGE". (Multiple rows of thumbnails are displayed.) This bug has already been addressed and will be fixed in the next version of Juicebox-Pro. In the meantime, try explicitly setting maxThumbRows="1". This should hopefully solve your problem.

Unfortunately, the Shopping Cart icon is not currently active in Small Screen Mode (which is used by default when the gallery is displayed on a mobile device).
Initially, the Shopping Cart icon was displayed only in conjunction with Fotomoto (before custom purchaseURLs were introduced) and the Shopping Cart button was disabled in Small Screen Mode as the Fotomoto popup interface does not fit on small screens. (This is noted in the 'Additional notes' of the Shopping Cart support section.)

This has been logged as a bug (the Shopping Cart icon should be disabled in Small Screen Mode only when Fotomoto is used and not when custom purchaseURLs are set) which should hopefully be fixed in a future version.
In the meantime, a possible workaround would be to set screenMode="LARGE" to force the gallery to be displayed in Large Screen Mode on all devices and in all browsers.

I'm not sure why the behavior of the plugin seems to change without you doing anything but a WP-Juicebox gallery will display all images attached to the page or post containing the gallery and the chart you refer to seems to be a .gif image attached to the post ('boat-specs-table.gif').
Please double-check the images attached to the post in question either in the Media Library itself or by editing the post, clicking the 'Add Media' button and selecting 'Uploaded to this post' in the 'Insert Media -> Media Library' section.

WP-Juicebox supports only one gallery per page or post.
If you want to embed multiple galleries on a single page or post, then you would need to do so manually following the baseUrl method documented here.

Set changeImageOnHover="TRUE" in the Pro Options text area of your gallery settings window.
(If creating a gallery with JuiceboxBuilder-Pro, this option can be found in the Main Image section.)

There are several contributing factors which will affect the speed at which your web page will load.
(1) The speed of the web server hosting the site.
(2) The speed of your own internet connection.
(3) The number of external files (JavaScript and CSS) that your web page loads.
(4) The file size of the gallery images.
(5) The value of the imagePreloading configuration option.

You have little or no control over #1 and #2 but you can certainly check the others.

#3 Check that your web page loads only external resource files that are required. If there are any redundant files (for example JavaScript libraries which are not actually used on the page), then remove them and this should help with the initial load speed.

#4 Make sure your image file sizes are not too large. When creating a gallery with JuiceboxBuilder-Pro using the default settings (of 1024px x 768px at 80% quality), the resulting images will likely be approximately 120KB each.
This is usually a good compromise between file size and image quality for web gallery use.
If your images are substantially larger than this, then you might like to try reducing the file size to see if this helps.

#5 Try changing the imagePreloading configuration option (in JuiceboxBuilder-Pro's 'Customize -> Main Image' section) from the default value of 'PAGE' to 'NEXT' so that when the gallery is initially loaded, only the next image in the gallery is downloaded and cached by the browser (rather than all the images on the current thumbnail page).

Hopefully these suggestions will help.

Many thanks for emailing me your complete gallery folder.

The spacing is actually caused by your images not being large enough to fill the gallery's image area (in a large browser window) and there is a gap at the top and bottom of the image in the gallery's image area. (This gap, in conjunction with the top of the thumbnail padding, accounts for the spacing you see.)
If you reduce the height of your browser window (so that the images need to be scaled down to fit within the image area) you should see the gap reduce until it is the same above and below the thumbnails (the only spacing left being the the thumbnail padding iteslf).

When using imageScaleMode="SCALE_DOWN" (the default setting), large images are scaled down to fit within the gallery's image area but small images are not scaled up (as their visual quality would be reduced).

Either increase the size of your images in your gallery or set imageScaleMode="SCALE".
Your landscape images are currently 640 x 479. The default values in JuiceboxBuilder-Pro are 1024 x 768 and this should be more suitable for your web gallery but you will need to feed JuiceboxBuilder-Pro larger source images in order for them to be resized down to 1024 x 758. Small images are not scaled up during the resizing process.

This should hopefully solve your problem.

Incidentally, if your browser window was much taller than it was wide, then you would also see space at the top and bottom of the main images.
Even using imageScaleMode="SCALE", the images would be scaled as large as possible to fit within the gallery's image area (without cropping) but, if the aspect ratio of the gallery is very different to that of the images, space can appear at the top and bottom of the images (or left and right, depending on the shape of the images).
For this scenario, please see this FAQ:
My Juicebox gallery shows too much space above or below the main image, how do I fix this?

Your gallery is too tall for your images. I would recommend setting your gallery's height to be a fixed pixel value so that the gallery's image area has an aspect ratio similar to that of the images themselves.

This problem may be related to server-side caching.
If caching is disabled on your web server, then Juicebox will have to download the images every time it needs them (as it will not be able to request them from a cache) and this may be causing the problem.
If you have an Apache web server and have a .htaccess file with an entry such as the following (to disable caching), then please try removing it to see if it helps.

Header set Cache-Control "max-age=0, private, no-cache, no-store, must-revalidate"

This may solve the problem (or at least hopefully point you in the right direction).

This might be difficult to achieve. There is no easy way to do this via configuration options. You might need to use JavaScript to remove all click and touch handlers from the gallery. However, I have not been successful in my own attempts to do this so, unfortunately, cannot provide any sample code that you can use.

If your images are stored in an array, then the easiest way to reverse their order is to use the PHP function array_reverse before you iterate over them to create your <image> entries, e.g:

$images = array_reverse($images);

If this does not help, then please let me see the code of your 'config.php' file so that I can take a look at at and hopefully help further.

Please see this FAQ:
My Juicebox gallery shows too much space above or below the main image, how do I fix this?

With a responsive site and a percentage height gallery, you do not know what size and shape the gallery will be (it will be dependent on the size and shape of the user's browser window). However, when using imageScaleMode="SCALE_DOWN" (the default value), you can be sure that Juicebox will scale the images down so that they are displayed as large as possible without cropping within the gallery's image area.
Please note that the size of the gallery is not determined by the size or aspect ratio of the gallery images. It is determined by the gallery dimensions and, if you use percentages, then also by the layout of your page (the dimensions of the gallery's parent containers).

Hopefully the suggestions in the FAQ will help.

With regard to padding, Juicebox has several padding options: stagePadding, imagePadding, imageNavPadding and thumbPadding. stagePadding and imagePadding are set to 0 by default.

If you are referring to the code in this forum post, then you can add your gallery's configuration options as attributes to the opening <juiceboxgallery > tag.
For example, you could change the line:

echo '<juiceboxgallery galleryTitle="Juicebox Gallery">';

... to something like:

echo '<juiceboxgallery galleryTitle="Juicebox Gallery thumbsPosition="TOP" autoPlayOnLoad="TRUE" captionPosition="BELOW_IMAGE">';

Alternatively, you can set configuration options in the JavaScript embedding code as noted here.