Reviving iPad Air from the dead
The issue in your video looks like it could be the Digitizer that's going bad. 

Disassembling iPad, especially the Air series, is a huge pain in the ass (it's Repairability score on iFitIt is 2/10). If you want to go that route here's the info from iFixIt: 

https://www.ifixit.com/Device/iPad_Air_Wi-Fi

Unlike the iPhones Apple doesn't replace the screens/digitizers because of the complicated repair process. They will however offer you a new iPad (same kind as what you have) with a Out Of Warranty exchange:

https://support.apple.com/ipad/repair/other