Q: iPhone 5s - some display issues

Hello,
not long ago I bought a used iPhone 5s because I was tired of my 4s. Everything was fine and I've got it for around 2 months now.
Now I experience a lot of image retention/burn in/persistence (whatever is right..). Often it happens when I use the Facebook app. Because the bottom and top bar are static and what I noticed: white. Only white/bright things burn in. The "burnt" area is around the edges, corners and not really in the middle. It lasts up to 30 minutes and goes away but happens really fast (5 minutes of using facebook/whatsapp = burn in).
Since two weeks I also have a little touch issue: When - for example - I am typing the screen goes unresponsive for less then 2 seconds but I can notice it.
Also sometimes the screen "darkens" a little bit but lights up again after seconds or minutes but not related to auto-brightness.
My screen has got a crack at the speaker, it goes from one side to the next but doesn't look to serious and I fixed it with some tape till I get a new screen.
Now I am asking myself if this IR-problem is based on the crack, hardware failure, software or maybe something else.
I tried alot from the internet (including wiping all data) but nothing worked..
Hope you can give me some advice!