My lumia 1520 did the same: phantom touch, screen jumping, navigation bar buttons flickering on and off, bing opening randomly. the phone was going crazy so much that i could not use it. I search everywhere for a solution. there is so many things people suggested like: changing setting, putting books on the phone to level it out if it's bend, hard reset and the list goes on, but non of that worked for me or seemed practical.
One thing i did read and notice, is that one member mentioned a screw missing under the sim/memory card trays. and sure i had a screw missing. after some research, if i understand correct that particular screw is the only screw that hold the back cover in place. why my phone didn't have a screw is a mystery. I don't know if this could be the problem, but i doubt it.
I eventually took my phone in for repair (was still under warranty at my service provider). they replaced my screen, and the phone is as fantastic as the first day i got it!
My advice: don't waste your time just take your phone in for repair