@chapt the ghost touch is a display assembly error. That might also be the cause for the rest of you issues but could also be related to the games you are playing. I would start with replacing it. Use something [link|https://www.youtube.com/watch?v=L0TQu9937_A|like this] video for the repair. New displays are readily available. Just do an online search and select a vendor of your choice.
While you work on your phone, take lots of pictures. Once you are done with it, take those pictures and create a guide for iFixit. That will help the next person that has a device with the same issues as you do. It's easy and fun to create these guides. https://ifixit.com/Guide/new The iFixit community will appreciate this.
Repair is War on Entropy!