If I use the relevant URL directly, I get a complaint that there is no config.xml (and indeed, there is not).
That's to be expected (on Google Drive or any other host). The 'full.html' file is for Juicebox's own internal use only (when a gallery is expanded in a new page of its own) and may not display the gallery when accessed directly (depending on the gallery's structure).
However, trying to access the 'full.html' page directly might actually be quite a good test.
This essentially takes Juicebox out of the equation. All we are trying to do is access an HTML file directly.
The HTML page should still be rendered by the browser (displaying the 'Config XML file not found.' message).
In my own gallery, going directly to the 'full.html' page in Mobile Safari on an iOS device:
https://7e149673cba79128b4d3fe7ac7a9b89 … /full.html
... displays the page (with the 'Config XML file not found.' message) as expected.
However, going directly to the 'full.html' page in your gallery in Mobile Safari on an iOS device:
https://3fd620ce7dd6a53cea4c9215317f4dd … /full.html
... displays the error 400.
Here are a few things to try.
(1) Change the content of the 'full.html' file (temporarily) to something like the following which has nothing at all to do with Juicebox and try to access the file directly in Mobile Safari to see if the same problem happens.
<!DOCTYPE html>
<html lang="en">
<head>
<title>Test</title>
</head>
<body>
<div id="test">Test text.</div>
</body>
</html>
If this still does not display correctly in Mobile Safari when accessed directly, then there may be an issue with the privacy settings on your 'full.html' file. Try making it private and then public again.
(2) Upload a completely new HTML file (with the sample code above) to the same directory as the 'full.html' file (your 'jbcore' folder) and see if you can access this directly in Mobile Safari. This should determine whether or not the problem is specifically with the 'full.html' file or with all HTML files in that directory.
(3) Try re-uploading your entire project to a new folder on Google Drive and ensure that all files and folders are made public.
The problem seems to be with access to the 'full.html' file on your Google Drive web space (both direct access and when Juicebox tries to access it dynamically) on iOS devices (but not in desktop browsers) so when I suggest that you try to access test pages directly (suggestions #1 and #2 above), you might want to use a service such as tiny.url to shorten the URLs and make life easier when entering the URLs into your Mobile Safari browser's address bar: http://tinyurl.com/
If we can figure out why the 'full.html' file cannot be accessed in Mobile Safari, then the other error 400 (which occurs when selecting a gallery from your menu) is likely to be related and hopefully the solution to one problem will fix the other.
Incidentally, I notice that your gallery's 'full.html' URL is much longer than mine. Maybe this has some relevance (especially when the 'juicebox.js' file is loaded and its code is run). Suggestions #1 and #2 above should tell us more.
If the problem does turn out to be due to the length of the URL, then there is little that can be done other than host your website somewhere other than Google Drive where you hvae more control over the path to your site.
If you have access to a regular web server, try hosting your web site there to see if everything works as expected. This should at least let us know whether or not the problem is somehow directly related to Google Drive (maybe with URL length or sharing settings).