Hi,
If your staging is set to push all files and data to the live when “publishing”, then it should be fine. I usually recommend using the license only on the staging site, if you are testing new updates there first, and then pushing to the live environment. You can have the license activated on both sites, but it is redundant if staging is always updated first.
I am not really sure about the mobile issue. I tested on a samsung phone, but all seems to be okay on my end – although I am not sure if I understand the problem correctly. I don’t exactly understand what do you mean by the “vanishing caption” in this case.