Sounds like either the touch IC on the screen has been moved or the digi has been broken in some place. I'd reccomend a new digi that should solve the touch issues, if it has the IC pre soldered makes the job a lot easier.

More than likely just gonna to leave a mark on the LCD it wont effect usage you will see it there in use though, 9 times out of 10 it'll all function fine with no issues

Would i be able to put the internals of a 5S into an SE body?

Looking they would fit and be mint but unsure