Although your post is entitled "Gesture Issues 1.3.2", I notice that your gallery is Juicebox-Pro v1.2.0.
Try upgrading your gallery to the latest version of Juicebox-Pro (v1.3.2) to ensure that any bugs that were present in v1.2.0 but which have since been fixed are not contributing to your problems.
There have been many bugfixes since v1.2.0. For a full list of changes, please see the Version History.
For instructions on how to get the latest version and how to upgrade existing galleries, please see the Upgrading Juicebox page.
I do not know if it will help with the problems that you reported but your web page also has HTML errors which should be fixed.
You can check the validity of your web page's code with the W3C Markup Validation Service.
user swipes and the whole page moves
Try upgrading your gallery to Juicebox-Pro v1.3.2 and fix the HTML errors on your web page to see if this helps.
Otherwise, check that there are no HTML elements on your web page which are stacked on top of your gallery and overlap it parts of it.
user single touches the image and is hyperlinked to the directed page, this is the same gesture for clicking the navigation arrows
When setting imageClickMode="OPEN_URL", the main image in the gallery acts like a standard HTML hyperlink (where a single tap on the screen is all that is required to open the URL, just like any other link).
If you single-tap on a navigation button, the image will change, if you single-tap elsewhere on the main image, the URL will be opened.
user swipes and the blue browser hotspots stay highlighted
This bug has been fixed in Juicebox-Pro v1.3.2.