Your gallery does not resize in Portfolio 2 because your gallery is embedded in two parent divs (.positionca95887172e34b94 and wrapper17986066c0979564), each with fixed widths of 1024px (set via CSS in your 'global_style.css' page).
Even though your gallery was a width of 100%, this means that it will be 100% of its parent container, ie. 100% x 1024px = 1024px. Therefore, the gallery's width will always be 1024px regardless of the size of the user's browser window.

If you want to use a side menu with a resizable gallery, please take a look at the View Resizable Gallery with Side Menu Example in the Resizable Gallery support section.

Set the 'Background Opacity' for your gallery to '0' (in the settings window).

The web page containing the gallery will contain the gallery's embedding code (as found here).
You would use a configUrl within the embedding code to point towards your PHP file so that Juicebox can find it, e.g.:

<!--START JUICEBOX EMBED-->
<script src="jbcore/juicebox.js"></script>
<script>
new juicebox({
configUrl: 'path_to_php_file/config.php',
containerId: "juicebox-container",
galleryWidth: "100%",
galleryHeight: "100%",
backgroundColor: "#222222"
});
</script>
<div id="juicebox-container"></div>
<!--END JUICEBOX EMBED-->

The XML file is where the list of images and captions is stored. Therefore, each gallery needs its own XML file (otherwise all galleries would display the same images and captions).
However, you could use the same PHP file to generate the XML data for different galleries by adding query string parameters to your configUrl to differentiate between galleries and so that the PHP file knows which gallery's information to gather, e.g.:

configUrl: 'path_to_php_file/config.php?id=12',

In the example above, you would get the 'id' within the PHP file (using $_GET['id']) and the PHP file would conditionally gather information from your chosen source depending on this value.

This would be a good idea. The principle is the same for Juicebox-Lite as it is for Juicebox-Pro so download Juicebox-Lite and try it out for yourself.

A gallery's files are usually all stored in the same directory for ease of use. Your gallery's files do not all need to be in the same directory but if you move them, then you may need to point towards them using configuration options such as configUrl, baseUrl and themeUrl. A list of these Embed Options can be found here.

The images and thumbnails for the gallery can be anywhere on your web server and they are pointed to via the imageURL and thumbURL entries in the XML file (which would need to be determined by your PHP file).

This FAQ (and the links within it) may also help:
Can Juicebox handle a custom data source, for example RSS or Instagram?

This needs to be done using server-side scripting (e.g. PHP).
For example, when Juicebox uses a PHP file to dynamically generate the XML data for a gallery, the server processes the PHP file and all that Juicebox sees is the XML data output from the PHP file (not the PHP code).
When trying to perform something similar client-side, Juicebox will see the actual JavaScript code (not the XML data).

If your tagged images do not show up in API searches within a couple of days, I would try removing and then re-adding the tags to your images.

This is not a Juicebox issue so Flickr should be hopefully be able to help.

Entering your Flickr User Id (83516242@N03) and your 'other work' tag into Flickr's API Explorer (bypassing Juicebox entirely) returns no images.
This is essentially the same method that Juicebox uses to fetch the images from Flickr's servers and if Flickr returns zero images, then Juicebox will not have any images to display in the gallery.

What you need to ask Flickr is why no images are being returned from an API search using:
user_id: 83516242@N03
tags: other work

It may just be that the tags have not yet fully propagated throughout Flickr's system.
According to this Flickr FAQ:

Juicebox-Lite uses the default values for all Flickr Pro Options. Therefore, the default Flickr sort order is DATE-POSTED-DESC. (These sort orders are Flickr terms. See the sort entry on this web page.)
Juicebox-Lite sends this value to Flickr as a parameter in an API search to fetch the images from their web server.
The images are then displayed in the gallery in the order in which they are returned by Flickr.
It looks like you are not the only one to have issues with Flickr's DATE-POSTED-DESC sort order.
Please see this Flickr forum thread.
Try changing the date posted on a couple of your images manually to see if this helps.
Select a photo, click on the three dots '...' to the bottom right of the photo, select 'Edit title, tags, and dates' and you can change the 'Date posted to Flickr' there.

Your custom theme file can be in any location you wish (whatever works best for you). It is loaded via the themeUrl configuration option and should not be included manually (in a <link> tag) in your web page.
The code I posted can be included in either your custom theme CSS file or in the HTML page containing the gallery. It should not make any difference.

I have created a test gallery using the following as a gallery's 'index.html' file and I do not see the problems you are describing:

<!DOCTYPE html>
<html lang="en">
    <head>
        <title>Juicebox-Pro Gallery</title>
        <meta charset="utf-8" />
        <meta name="apple-mobile-web-app-capable" content="yes" />
        <style type="text/css">
            body {
                margin: 0px;
            }
            #jb-glry-dlg:fullscreen {
                background-color: #000000;
            }            
            #jb-glry-dlg:-moz-full-screen {
                background-color: #000000;
            }            
            #jb-glry-dlg:-webkit-full-screen {
                background-color: #000000;
            }            
        </style>
    </head>
    <body>
        <!--START JUICEBOX EMBED-->
        <script src="jbcore/juicebox.js"></script>
        <script>
            new juicebox({
                containerId: 'juicebox-container',
                galleryWidth:' 400',
                galleryHeight: '400',
                backgroundColor: 'rgba(0,0,0,0)',
                useFullscreenexpand: 'true'
            });
        </script>
        <div id="juicebox-container"></div>
        <!--END JUICEBOX EMBED-->
    </body>
</html>

I have uploaded the gallery here. [Gallery removed.]
The fullscreen functionality works fine in all browsers I have tested it in (Firefox 23.0.1, Chrome 29, Opera 16, Opera Next 16 and Safari 5.1.7) and the background is black in every case. Additionally, the layout of the gallery is fine in all browsers including Safari.

Keep a copy of the gallery on your computer and you can edit it using JuiceboxBuilder-Pro.
You can add or remove images on the 'Images' tab and then re-upload the gallery to your web server when finished.
If you make no other changes to the gallery than adding or removing images, then you need only re-upload the gallery's 'config.xml' file and the new images and thumbnails.
If you simply upload your entire gallery to your web server, most FTP programs should be smart enough to upload only new or changed files (though you may want to manually delete images and thumbnails that are no longer included in your gallery).

If the captions are positioned on the image overlay (OVERLAY or OVERLAY_IMAGE), then set showOverlayOnLoad="FALSE" in your gallery's XML file (in JuiceboxBuilder-Pro's 'Customize -> Main Image' section).

No problem.
I'm glad everything is working as expected just now.

According to the 'Inspect Element (Q) -> Style Editor' list in Firefox 23.0.1, the 'jbcore/classic/theme.css' file is not being loaded on your web page (only the 'jbcore/delosgaia/theme.css' file).

Likewise with 'F12 -> Resources -> Stylesheets' in Chrome 29.
The 'jbcore/delosgaia/theme.css' file is listed but the 'jbcore/classic/theme.css' file is not.

Can you provide some steps that I can reproduce to find out where you are seeing that the 'jbcore/classic/theme.css' file is being loaded?

If the 'jbcore/classic/theme.css' file is being loaded in your web page (though it should not be and my checks above seem to confirm this) and it is somehow conflicting with your modified theme, then a quick fix might be to simply delete the file.
Otherwise, if you need to use the original 'jbcore/classic/theme.css' file in other Juicebox galleries in other web pages, then try renaming the file and point to it using a themeUrl in the galleries which require it. In doing so, the Juicebox gallery on the page you quoted will no longer be able to load the original 'theme.css' file (as there will be nothing in the default themeUrl path and the gallery will not know of any themeUrl used in other galleries in other web pages).