The gallery sizing issue in iOS 7 has now been fixed in Juicebox v1.3.3. Please see the Version History for a full list of changes and the Upgrading Juicebox page for details on how to get the latest version.

The easiest solution (if both the backButton and galleryTitle are positioned on the OVERLAY) would be to set backButtonHAlign="LEFT" and galleryTitleHAlign="CENTER" (or vice versa). (An alternative solution would be to set backButtonPosition="TOP" and galleryTitlePosition="OVERLAY".)

You should be able to tweak the position of either the Back Button or the Gallery Title via CSS as follows:

<style type="text/css">
    /* Back Button */
    .jb-go-back {
        margin-left: 100px !important;
    }

    /* Gallery Title */
    .jb-area-large-mode-title {
        margin-left: 150px !important;
    }
</style>

No. This is not possible.

We did not write the Juicebox module for Drupal ourselves and, unfortunately, I am unfamiliar with its code.
Please post your query in the Drupal forums where the author of the module should be able to help you out.

@guuz

If you just want the image to open in a new tab/window when clicked, set imageClickMode="OPEN_URL".
When an image is clicked, the corresponding linkURL will be opened in a tab/window specified by the linkTarget attribute.
You might like to take a look at this forum post which details how to have each image appear in a lightbox-style overlay when clicked.

Thank you for providing the URL to your gallery.
It looks like your problem is caused by global CSS rules in your 'style.css' file. In this file you have the following code:

img, object, embed, video {
    max-width: 100%;
    left: 75px;
    right: auto;
    margin-top: 10px;
    margin-left: 5px;
    position: relative;
    float: left;
}

These CSS rules will apply to all images on your web page (including those in your Juicebox gallery). Juicebox has no option but to inherit such global rules.
These rules should be applied only to those elements on your web page which require them through use of CSS classes and ids.
If you were to remove the code above (just as a test), you should hopefully see that the gallery functions correctly and your images are no longer shifted to the right (resulting in cropping).

Give each 'juicebox-container' <div> a unique 'id' and refer to that 'id' in the gallery's containerId configuration options.
For example:

<!--START JUICEBOX EMBED-->
<script src="http://www.mywebsite.com/_juicebox/First-Gallery/jbcore/juicebox.js"></script>
<script>
new juicebox({
baseUrl : "http://www.mywebsite.com/_juicebox/First-Gallery/",
containerId : "juicebox-container-one",
galleryWidth: "560",
galleryHeight: "750",
thumbWidth: "50",
thumbHeight: "50",
backgroundColor: "rgba(255,255,255,1)"
});
</script>
<div id="juicebox-container-one"></div>
<!--END JUICEBOX EMBED-->

Some other text here. Some other text here. Some other text here.
Some other text here. Some other text here. Some other text here.
Some other text here. Some other text here. Some other text here.

<!--START JUICEBOX EMBED-->
<script>
new juicebox({
baseUrl : "http://www.mywebsite.com/_juicebox/Gallery-Two/",
containerId : "juicebox-container-two",
galleryWidth: "560",
galleryHeight: "750",
thumbWidth: "50",
thumbHeight: "50",
backgroundColor: "rgba(255,255,255,1)"
});
</script>
<div id="juicebox-container-two"></div>
<!--END JUICEBOX EMBED-->

Incidentally, you need to load only one instance of the 'juicebox.js' file on your page and your baseUrls should end with a trailing slash.

As long as 'Crop To Fit' is deselected in JuiceboxBuilder-Lite, images should not be cropped in a Juicebox-Lite gallery under any circumstances that I can think of.
In order to help further, I would really need to see the gallery in question so please upload it to a server and post the URL so that I can take a look and help further.

Are you talking about using the browser's back button to "go back to the JB gallery"? If so, this is likely to be a browser caching issue which may be unavoidable.
If you go back to the gallery via a link (the URL that brought you to the unexpanded gallery in the first place), then the gallery should display OK.

The Back Button may not be the only link in a gallery.
A user may have set imageClickMode="OPEN_URL", in which case each main image will be a link.
Also, links may have been embedded in the Gallery Title or in image titles or captions using HTML formatting as documented here.
Unfortunately, disabling the Back Button in fullscreen mode will not help in these scenarios.

Please note that I have just edited the code above so that it should not interfere with the Small Screen Mode rendering of the gallery. (During testing, I noticed that the Splash Page text area was offset using the original code.)

The default value for imageScaleMode (used by Juicebox-Lite) is SCALE_DOWN so images should not be cropped in a Juicebox-Lite gallery.

These are options used by JuiceboxBuilder-Lite to prepare the images for the gallery (rather than configuration options used by Juicebox-Lite itself to display the images in the gallery). Setting 'Crop to Fit' will crop your images before they are used in the gallery.
Take a look inside your gallery's 'images' folder to see if the images themselves look like cropped versions of your original images. If they are, then remake your gallery in JuiceboxBuilder-Lite (using your original images as the source) and ensure that the 'Crop To Fit' checkbox is not selected on the 'Images' tab (but keep the 'Resize Images' checkbox selected).
If the 'Resize Images' checkbox is not selected, then JuiceboxBuilder-Lite will simply copy your original images across to the output 'images' folder without resizing them. This may not be suitable if your original images are large.

The thumbsVAlign configuration option vertically aligns the thumbnails within the thumbnail area.
If you change your gallery's captionPosition from 'BELOW_IMAGE' to 'BOTTOM', this will bump the thumbnails up a bit as the thumbnail area will no longer extend to the bottom of the gallery but just to the top of the caption area.

I would not recommend trying to tweak the position of a gallery element using CSS as it is likely to have unwanted knock-on effects. For example, when the browser window is resized and elements need to be redrawn, Juicebox will not know of your manual modifications and will not be able to take them into account.
However, if you really want to try it (and as your gallery has fixed dimensions, it may work OK), you could try adding the following CSS to the <head> section of your web page:

<style type="text/css">
    .jb-flag-large-screen-mode .jb-idx-thumbnail-container {
        margin-top: -50px !important;
    }
    .jb-flag-large-screen-mode .jbn-nav-button.jbn-left-button.jbn-nav-button-icon {
        margin-top: -50px;
    }
    .jb-flag-large-screen-mode .jbn-nav-button.jbn-right-button.jbn-nav-button-icon {
        margin-top: -50px;
    }
</style>