Sounds grave. I would guess, it might rather be the display than the OS, as all faults seem to be connected to the touch-screen. The errors occuring after updating to Android 7 might just be coincidence.
Especially the partially not responding screen is a known issue.
You might want to check the Fairphone troubleshooting tool (display > the touch function is defect):
Or you might do some reading in this (rather long) thread:
To check things out, you could try replacing the display. As I guess, you don’t have a second one putting on dust in your drawer, you could turn to a friend with a FP2 or to one of the georgeous fairphoneangels in your area. In case there are no angels around, you might post a request for help in this forum, giving a region that would be ok for you.
Finally; I can’t find the errors in the wiki concerning Android 7 issues: