1. When I view your gallery on my own iOS mobile device, I see the Splash Page (rather than a thumbnail page showing a grid of thumbnails). If you have changed your gallery's configuration options recently, try clearing your browser's cache before reloading your gallery's web page to ensure that your browser is fetching the latest gallery files from your server (instead of perhaps using older cached versions).
2. After a gallery has been expanded from the Splash Page, the user can click the Expand/Close Button (on the gallery's Button Bar) to return to the embedding page. Just be sure to set showExpandButton="TRUE" (in JuiceboxBuilder-Pro's 'Customize -> Lite' section). You'll also need to make sure that you do not set buttonBarPosition="NONE" ('Customize -> Button Bar'). You can see the Expand/Close button in the top right corner after expanding this demo gallery from its Splash Page.
3. It can sometimes be difficult to scroll past an embedded gallery. If you initiate a scrolling swipe on a gallery, then unless you are very precise with your up or down motion, the gesture may be interpreted by Juicebox as the start of a navigation swipe (to go 'previous' or 'next' on a thumbnail page or a main image). This will not be a problem when the Splash Page is displayed. It may only be a problem when the gallery is embedded without the Splash Page (screenMode="LARGE" or showSplashPage="NEVER").
4. captionPosition is a Large Screen Mode configuration option only. (This is noted in the description for captionPosition in the Caption Options section of the Config Options page). In Small Screen Mode (on mobile devices), captionPosition is always set to OVERLAY (where the caption area sits at the foot of the gallery and spans the width of the gallery). This gives the captions as much room as possible on mobile devices.
I notice that your gallery currently uses Juicebox-Pro v1.4.3.2. You might like to try upgrading your gallery to the latest version (v1.5.0) as many bugs have been fixed (and new features introduced) since v1.4.3.2. (Depending on the mobile device you are using to view your galleries, this might help with your first query above.) For reference, a list of changes between versions can be found on the Version History page. Full instructions on how to download the current version and upgrade existing galleries can be found on the Upgrading Juicebox support page.