Try creating an .htaccess file containing the following code and upload it to your website's root directory. (Please note that this requires an Apache web server.)

<IfModule mod_headers.c>
Header set Cache-Control "no-transform"
</IfModule>

This should prevent content modification on your site when visitors view your galleries over a 3G connection.

You could also contact your 3G provider to see if it is possible for content modification to be turned off on your account (although this will help only when you view other people's galleries and will not solve the problem of other people viewing your own galleries over their own 3G connections, which the solution above tackles).

OK, no problem.
Thanks for letting me know.
(It should work fine, though. I've tested it myself.)

The problem is likely to be due to your gallery being loaded on your web page as soon as the page is displayed but the container for the gallery not being visible/displayed until the 'Photo Gallery' tab is selected and so Juicebox (when it is loaded) cannot determine what its size should be.

Try changing your gallery's dimensions from percentages to absolute pixel values to see if this makes a difference.
If it works but you would rather keep percentage dimensions, try loading the gallery on demand (rather than when the page is initially displayed).

Change your embedding code to the following:

<!--START JUICEBOX EMBED-->
<script src="h_i_slide/jbcore/juicebox.js"></script>
<script>
    function loadGallery() {
        new juicebox({
            containerId : "juicebox-container",
            baseUrl : 'h_i_slide/',
            galleryWidth: "100%",
            galleryHeight: "100%",
            backgroundColor: "rgba(252,242,204,100)"
        });
    }
</script>
<div id="juicebox-container"></div>
<!--END JUICEBOX EMBED-->

... and change line 237 from:

<li class="TabbedPanelsTab" tabindex="0"><a href="#gallery">Photo gallery</a></li>

... to:

<li class="TabbedPanelsTab" tabindex="0"><a href="#gallery" onclick="javascript: loadGallery(); return true;">Photo gallery</a></li>

I am unable to replicate the problems you describe in test galleries of my own so the problems may be related to the non-gallery code on your web page.

Here are a couple of things to try which may help:

• Try completely clearing your browser caches to ensure that your browsers are fetching and using the most recent versions of your gallery files from your web server.

• If you want to keep expandInNewPage="TRUE", try setting useFullscreenExpand="FALSE" to see if this makes a difference.

• Try checking the HTML code on your web page with the W3C Markup Validation Service and fix the errors reported. (There are currently over 300 errors reported but many are duplicates of others and it should hopefully not take too long to go through the list).

• Your web page loads an old version of jQuery (v1.7.2). Try upgrading this to the current stable version (v1.10.2) and update any other out-of-date external JavaScript files. (If there is a conflict between one of your web page's JavaScript files and the 'juicebox.js' file, then updating the files in question may help.)

Even if these suggestions do not completely solve your problems, it would be wise to fix the errors on your web page and update the external JavaScript files. Once these have been done, we can eliminate them from the problem.

If the problem persists, then to check for a possible conflict between one of your web page's JavaScript files and the 'juicebox.js' file, try removing all the external JavaScript files from your page to see how the gallery reacts and then reintroduce them one-by-one until you find the source of the problem.

There are a couple of things you can do to speed up the initial loading of a gallery:
(1) reduce the file size of your images (by reducing either their resolution or quality), or...
(2) change the imagePreloading configuration option (in JuiceboxBuilder-Pro's 'Customize -> Main Image' section) from the default value of PAGE (which preloads all images on the current thumbnail page) to NEXT (which preloads only the next image in the gallery).
(There are other factors, such as the speed of your web server and internet connection, which you essentially have no control over.)

That's the thumbnail paging text. All your thumbnail dots are on the same (single) thumbnail page so the thumbnail paging text will always read '1 of 1'.
If you want to remove the thumbnail paging text, set showThumbPagingText="FALSE" (in JuiceboxBuilder-Pro's 'Customize -> Thumbnails' section).

If you would like the image numbers (e.g. '1/4') to be displayed as part of the image captions, set showImageNumber="TRUE" (in JuiceboxBuilder-Pro's 'Customize -> Caption' section).

All gallery files must be on the same domain (or subdomain) as the page containing the JavaScript embedding code due to the same-origin policy. Please see this web page for further details.

If you intend to embed your gallery into a page on parlamer.net, then your gallery files must also be on this domain (and not parlamer.fr).

The only way around this would be to load your gallery into an iframe, as documented as Option #2 here.

It should hopefully be relatively easy to implement the Responsive Multi-Level Menu by using the template in my first post above, loading the required Responsive Multi-Level Menu external CSS and JavaScript source files in the <head> section of the page, replacing the contents of the 'menu' <div> with the required Responsive Multi-Level Menu entries and adding the snippet of JavaScript code (from the Responsive Multi-Level Menu sample HTML files) before the closing </body> tag.
You can also reduce the width of the 'menu' <div> so that the Responsive Multi-Level Menu icon does not take up too much screen real estate.

Within a gallery's embedding code, you can change the size of the gallery container (via the galleryWidth and galleryHeight configuration options) but not where it appears in the embedding web page.
The positioning of a gallery within a web page is dependent entirely on the code of the web page itself (and where in the web page you paste the embedding code).

If you post the URL to your web page I can take a look and perhaps suggest a way to move your gallery further up your page.

You could use an image as the Gallery Title and center it horizontally in your gallery by setting galleryTitleHAlign="CENTER". Please see the Adding a Logo support section for further details.

Alternatively, you could use an image as the Back Button itself by using settings such as:

backButtonPosition="TOP"
backButtonUseIcon="FALSE"
backButonUrl="http://www.example.com/"
backButtonText="<img src="logo.png" width="100" height="50" alt="logo" />"

If using JuiceboxBuilder-Pro to create your gallery you could just enter something like the following into the backButtonText field (JuiceboxBuilder-Pro will escape the necessary characters for you):

<img src="logo.png" width="100" height="50" alt="logo" />

It is not possible to tile/repeat an image as a gallery background using the Background Image Options.
You would need to set your gallery's background to be transparent (setting backgroundColor: 'rgba(0,0,0,0)'  in the embedding code) and set your background image on your embedding web page via HTML and CSS using the CSS background-repeat property.

I have just noticed you have no commas separating the backgroundColor from the baseUrl in your gallery's embedding code.
(I copied and pasted your code and changed only the paths.)
I have now corrected the code in my post above.

If it still does not work, please post the URL to the web page into which you are trying to embed your gallery so that I can take a look and help further.

The link you posted comes up with a 'Page not found' message.

However, it sounds like your current WordPress theme uses the CSS border-box model which currently breaks the Juicebox layout. (This will be fixed in the next version of Juicebox.)
To implement the fix manually, open the 'wp-juicebox/jbcore/classic/theme.css' file in a plain text editor and add the following code to the file:

.juicebox-gallery h1, .juicebox-gallery h2, .juicebox-gallery h3, .juicebox-gallery h4, .juicebox-gallery div, .juicebox-gallery p, .juicebox-gallery span{
    -webkit-box-sizing: content-box;
    -moz-box-sizing: content-box;
    box-sizing: content-box;
}

Hopefully this will solve your problem.