What you are looking to achieve could probably be achieved quite easily without the need to pass any image ids as parameters or use iframes (although it would need to be set up manually and could not be done with the existing WP-Juicebox plugin which is designed to embed Juicebox galleries directly into WordPress pages or posts).

You could create your galleries using JuiceboxBuilder-Pro (on your computer).
Upload the complete gallery folders (not just the contents) to your web server. It does not matter where you upload them to as long as you know where they are.
Just insert image links in your WordPress pages or posts to point to each gallery's 'index.html' file.

For example, if you uploaded a complete gallery folder named 'gallery1' to the root directory of your web server, then you could use an image link such as the following.

<a href="/gallery1/index.html"><img src="/images/thumbnail.jpg" width="80" height="60" alt="thumbnail" /></a>

(You would need to provide a suitable thumbnail image to use as a link.)
When the user clicks on a link, the browser would be redirected to the gallery's 'index.html' page which would display the gallery on a page of its own.
Your gallery could incorporate a Back Button to allow the user to return to the original WordPress page or post containing the link.

This is a known issue which has already been addressed and will be fixed in the next version of Juicebox. However, just fior the record, there are other limitations of using an iframe which are documented in the 'Using an iframe' support section here.

I hope this helps.

If you want a gallery to completely fill a users browser window, make sure that it is the only element on your web page and set its dimensions to 100% x 100%.

You can insert links into image captions by using HTML formatting as documented in this FAQ:
How do I add HTML formatting to image captions and titles?

For example, you could enter a caption such as the following into JuiceboxBuilder-Pro.

<a href="http://www.example.com/index.html">Link text goes here</a>

It may not be ideal to use image captions as navigation for your site (it depends on your site).
You may have better luck following one of the resizable templates here (placing your navigation menu in the header).

Unfortunately, there is no easy way to use images uploaded for NextGEN galleries in a WP-Juicebox gallery (other than to activate the NextGEN plugin and use the NextGEN Gallery Id in your gallery settings window).
WP-Juicebox is not designed to accept a folder of images as a source of images for a Juicebox gallery.
The plugin would need to be re-written to handle a new image source (which would also need to take into consideration thumbnails and captions).

You would need to either create new WP-Juicebox galleries by re-uploading the images to your Media Library or download all your images to your computer, create Juicebox galleries there and then upload them to your web server and embed them in your WordPress pages and posts manually.

Hopefully the following notes will help.

If you want the images in your gallery to be displayed in full (without cropping), set imageScaleMode to either SCALE_DOWN or SCALE (in JuiceboxBuilder-Pro's 'Customize -> Main Image' section).

Please take a look at the Using a Resizable Gallery with a Header support section. The View Resizable Gallery with Top Menu Example has a header of fixed height and the gallery takes up the remainder of the user's browser window. You can view the source of the web page in a browser and copy/modify the code to suit your own needs (by swapping the sample header content for your own navigation menu).
It might not be exactly what you want but if you want to overlay a transparent navigation menu on top of a Juicebox gallery, then knowledge of HTML, CSS (and perhaps JavaScript) would be required. It would not be something that could be implemented within Juicebox itself.
You could, however, embed links into the Gallery Title or Back Button as noted in these FAQs:
How do I add HTML formatting to the Gallery Title or Back Button?

If you want a Juicebox gallery to start an automated slideshow as soon as it loads, set enableAutoPlay="TRUE" and autoPlayOnLoad="TRUE" ('Customize -> AutoPlay'). You may also want to set enableLooping="TRUE" ('Customize -> General').

Use the following settings:

buttonBarPosition="NONE"
galleryTitlePosition="NONE"
backButtonPosition="NONE"
showImageNav="FALSE"
captionPosition="NONE"

Use the following settings:

showThumbsOnLoad="FALSE"
showSmallThumbsOnLoad="FALSE"
showThumbsButton="FALSE"
showSmallThumbsButton="FALSE"

Make sure that your gallery's dimensions match the aspect ratio of your images (so that there is no wasted space around your images within the gallery).

I'm not entirely sure what you mean by this. You can set captionPosition="OVERAY_IMAGE" so that the image titles and captions appear on the image overlay (on top the the main image). However, the text will appear towards the bottom of the image, not the side.

You'll need to set backButtonPosition to either TOP or OVERLAY.
If you do not set backButtonPosition, then Juicebox will use its default value of NONE and the Back Button will not be displayed (regardless of any of the other Back Button options which may have been set).
For reference, a list of all Back Button configuration options can be found here.

Set showImageNumber="FALSE" in JuiceboxBuilder-Pro's 'Customize -> Caption' section.

One thing that these galleries have in common is that neither completely fills the browser window.
However, if this was somehow a contributing factor, then I would expect you to see the flickering in other galleries which do not completely fill the browser window (such as the Flat Design and Top-Left Alignment demo galleries).
The two galleries you see the flickering in have much in common with other demo galleries on the page which you do not report seeing the flickering in so, at the moment, I am unable to draw any conclusions as to what the problem might be.

It certainly seems to be.
Out of interest, what operating system and version of Safari do you use?
If you are not already using the latest version of Safari for your system, try updating it to see if this helps.

If you set a high enough 'z-index' value to your menu, it should be stacked on top of the gallery and function as expected.
Try adding the following code to the <head> section of your web page:

<style type="text/css">
.pure-menu ul {
    z-index: 9999 !important;
}
</style>

I do not know the original reason for giving WP-Juicebox its own shortcode but I guess it would allow for additional attributes to be added at a later date (perhaps for new functionality in future versions) without hijacking WordPress's own gallery shortcode.

Please post suggestions for future versions of Juicebox in the Feature Request forum thread
It keeps them all together and ensures that they are not overlooked.
Thank you.

It sounds like the problem is likely to be a JavaScript conflict between Juicebox and Foundation 5 (or a bug in the Windows Phone browser).

WordPress has its own wp_is_mobile() function so if you wanted to prevent the 'juicebox.js' JavaScript file from being loaded on your pages, then you could open the 'wp-juicebox/wp-juicebox.php' file in a plain text editor and wrap line 28 in the wp_is_mobile() function (allowing add_action() to be run only if wp_is_mobile() returns false):

if (!wp_is_mobile()) {
    add_action('wp_enqueue_scripts', array(&$this, 'add_scripts_wp'));
}

If you have a more specific function which checks for a Windows Phone, then you could use this instead of wp_is_mobile().

With regard to the Juicebox shortcode which is already in the post, you would want WordPress to replace it with nothing (an empty string). Ordinarily, if you just disabled the add_shortcode() function on line 41 of the 'wp-juicebox.php' file (using the same method as above), then WordPress would simply display the Juicebox shortcode as plain text in the post.
In order to work around this, you would need to add the following to the very beginning of the shortcode_handler() function on line 219 of the 'wp-juicebox.php' file:

if (!wp_is_mobile()) {
    return;
}

Again, replace wp_is_mobile() with your own more specific function.

What you are currently doing is possibly the best solution.
If you want to dynamically change a configuration option, then it is certainly much easier to do so by setting the option in the embedding code (via a JavaScript variable) rather than try to set it in the gallery's XML file.
Also, it is not possible to change the value of a configuration option once the gallery has been loaded so the only option would be to reload the gallery with the new value (as you are doing).