The only oddity I see on your web page at the moment is that your embedding code (for your November gallery) is enclosed in CDATA tags and that the closing tag has its final > character escaped as > in the following line:

// ]]&gt;</script></p>

It may (or may not) make a difference but try either replacing the line above with:

// ]]>
</script>
</p>

... or completely remove the CDATA tags around the JavaScript code.

Is it OK in both Chrome and Mobile Safari on the iPad? What iOS does your iPad run? Perhaps you can upgrade the version of iOS on your iPhone (if it is not already up-to-date) to see if this makes a difference. (By checking both Chrome and Mobile Safari in both an iPhone and an iPad and checking which version of iOS each device is running, you may at least be able to find a pattern within iOS devices.)

As you seem to be embedding your galleries manually (rather than using WP-Juicebox), then perhaps a workaround would be to upload your gallery folders to your web server and include links to them within your posts (rather than embed them directly in your posts).

My suggestion was not to replace the line:

winWidth = window.innerWidth ? window.innerWidth : $(window).width();

... but to make the adjustment after it, e.g.:

winWidth = window.innerWidth ? window.innerWidth : $(window).width();
winWidth = winWidth - 20;

The code which determines the window width will return the result in pixels so you should stick to using a pixel value for this right-hand border so you can subtract the border (px) from the window width (also px).
Also, when making the adjustment to the winWidth value, the code will be purely arithmetic so you should not use a suffix, such as px. (I used a suffix in my original code above but I have corrected the error. Sorry for any inconvenience.)
Use a CSS border such as:

body {
    margin-right: 20px;
}

... and then use either:

winWidth = window.innerWidth ? window.innerWidth : $(window).width();
winWidth = winWidth - 20;

... or:

winWidth = window.innerWidth ? window.innerWidth - 20 : $(window).width() - 20;

I have tested this myself and it seems to work fine.

The Showkase Acqua Photo demo uses Juicebox-Pro. (The Juicebox galleries within the demo use Pro options such as AutoPlay and hiding thumbnails.)

To achieve this, you would need to either:
(1) Purchase Showkase-Pro (which comes with Juicebox-Pro)
... or:
(2) Purchase Showkase-Standard and Juicebox-Pro separately

You can change the rollover tooltip text using the languageList configuration option. Please see here for details.
Change the default 'Go Back' text to whatever you like and add the languageList configuration option as an attribute to the opening <juiceboxgallery> tag in your gallery's XML file.
For example:

<juiceboxgallery
    galleryTitle="Juicebox-Pro Gallery"
    languageList="Show Thumbnails|Hide Thumbnails|Expand Gallery|Close Gallery|Open Image in New Window|Next Image|Previous Image|Play Audio|Pause Audio|Show Information|Hide Information|Start AutoPlay|Stop AutoPlay|AutoPlay ON|AutoPlay OFF|Email|Buy this Image|Share on Facebook|Share on Twitter|Share on Google+|Share on Pinterest|Share on Tumblr|of"
>

The backButtonText configuration option is only for use when using text for the Back Button instead of an icon (not for the rollover text which is handled by the languageList configuration option).

Please post the URL to your gallery so that I can take a look for myself and help further.

Yes.

Open your gallery's 'config.xml' file in a plain text editor and add the languageList configuration option as an attribute to the opening <juiceboxgallery> tag.
For example:

Juicebox-Pro already includes a shopping cart icon (for Fotomoto support). You can use this icon instead of the default 'Open Image in New Window' icon by opening the 'jbcore/classic/theme.css' file in a plain text editor and changing line 721 from:

content: "\e004";

... to:

content: "\e00e";

You currently have Showkase-Standard.

To be able to create Juicebox-Pro galleries (with no branding or image limit) with Showkase you could either:
(1) Purchase Juicebox-Pro from here and upgrade your Showkase installation by following the instructions here.
... or:
(2) Purchase Showkase-Pro (which comes bundled with Juicebox-Pro and SimpleViewer-Pro) and we can refund you for your Showkase-Standard purchase. (If you decide to do this, please let me know and I will send you an email so that you can forward me your transaction details for a refund.)

Please note that the only difference between Showkase-Standard and Showkase-Pro is that Showkase-Standard comes bundled with Juicebox-Lite and SimpleViewer-Standard (the free versions of the image viewers) whereas Showkase-Pro comes bundled with Juicebox-Pro and SimpleVIewer-Pro.

If you purchase Showkase-Standard and upgrade it manually with Juicebox-Pro and SimpleViewer-Pro, then you will end up with exactly the same files as if you had purchased Showkase-Pro.

You can set only a single font for gallery text using the galleryFontFace configuration option (in JuiceboxBuilder-Pro's 'Customize -> General' section).

If you want to use multiple fonts throughout your gallery, you can override the galleryFontFace by using HTML formatting (for elements such as the Gallery Title, Back Button and image titles and captions) as documented in these FAQs:
How do I add HTML formatting to image captions and titles?
How do I add HTML formatting to the Gallery Title or Back Button?

I would recommend saving preset XML files in a folder dedicated to preset XML files and then save each gallery into a separate folder. This should keep your preset XML files separate from your gallery files.

If you like, you can keep each gallery in its own individual folder, upload your complete gallery folders (not just the contents) to your web server and embed the galleries into your web pages using the baseUrl method of embedding.
Keeping each gallery in its own folder may help to keeps things organized on your web server.

You have purchased and are using Showkase-Standard (not Showkase-Pro).
You can check by looking at the text below the login panel on your Showkase admin login page. (Showkase-Standard displays only 'Showkase 1.2.0' whereas Showkase-Pro displays 'Showkase-Pro 1.2.0'.
Showkase-Standard comes bundled with Juicebox-Lite and SimpleViewer-Standard (the free versions of the image viewers) and Showkase-Pro comes bundled with Juicebox-Pro and SimpleViewer-Pro. (The only difference between Showkase-Standard and Showkase-Pro is the bundled viewers.)

You need to swap the entire Lite 'jbcore' folder in your 'showkase/admin/plugins/juicebox/master/' directory with the Pro 'jbcore' folder from the Juicebox-Pro download zip package ('juicebox_pro_1.3.3/web/jbcore/').

If your galleries are limited to 50 images and you see the Juicebox badge/link at the bottom-right corners, then your galleries are Juicebox-Lite galleries, not Juicebox-Pro. (Juicebox-Pro does not contain an image limit or branding.)

Instructions for upgrading Showkase to use a Pro viewer can be found here.
Be sure to rebuild your existing galleries after upgrading ('Pages (tab) -> Edit (gallery page)-> Advanced (tab) -> Rebuild this Juicebox gallery').

The page you linked to is a Drupal page.
Drupal is a Content Management System whose pages are not designed to fit completely within a user's browser window.
Vertical scrolling is normal and (on most Drupal pages) necessary to view all content on the page.
It would not be possible to constrict all content on a Drupal page to fit within a user's browser window (no matter what its size) without any scrolling.

You would have to manually construct your web page using the View Resizable Gallery with Top Menu Example sample gallery as a template. You can view the source of the web page in a browser, copy it and swap the header, gallery and footer for your own content.

Alternatively, you could try just reducing the height of your gallery (in your Drupal page) so that less vertical scrolling is necessary for most users.

[Post split to new thread.]

With Juicebox-Lite (the free version), it is not possible to add padding to a gallery from within the plugin's interface.
However, if you purchased Juicebox-Pro (and upgraded the plugin following the 'Upgrading to Juicebox-Pro' instructions on this web page), you would have access to the imagePadding and stagePadding configuration options which you could enter into the plugin's 'Pro Options' text area.
Please note that both imagePadding and stagePadding add padding to all four sides of the image and stage respectively (not just the top).

For reference, a list of all available configuration options can be found here.

Otherwise, you could edit the gallery's 'index.html' page after the gallery has been created and add padding above the gallery using CSS.

Unfortunately, the security restrictions in IE11, Chrome and Opera which prevent the loading of local XML files cannot be circumvented and so there is no possibility of previewing Juicebox galleries locally in these browsers (without using emulation).
As such, there is nothing we can do to allow users to preview Juicebox galleries locally in IE11 (or Chrome or Opera) in the future.

As arachnid says, you can use 'F12 -> Emulation -> Document Mode -> 10' (to emulate IE10) within IE11 (or use Firefox or Safari).