I see from your list of things you have done, that you haven't yet reset your iPad to its factory default condition. This has helped quite a few iPad users, according to what they've told me. You'll need to use your iTunes program to do this to get a clean install. You'll need to turn off your anti-virus program on your computer, and be sure you do your backup first, and also that you understand what is backed up and what is not!
Here are the links for understanding and doing a backup, and the last link is the one for resetting to factory default condition ...
When you restore your backup, if the problems return, then you'll have to reset to factory default again, but this time do not restore your backup to verify whether the problem shows up in the factory fresh condition or not. If it does show up, then you'll need to take it to Apple Support, in that condition (without your data or apps on there) and have them sort it out for you.
If it doesn't show up there in its factory default condition, but it does when you restore your backup, then you'll know that it's a problem with one of your apps or some data or file corruption in your data and you'll have to eliminate the problem from your own data first.