This is a very clear thing. The name of the rare things are ''Ghost touch". From the moment you dropped your phone it goes wild. That is definitely screen damage, the screen may be not cracked or something but from the inside it is. The only way to solve this problem is to replace your screen.
No, if you wanna remove the front camera you have to remove the ''front camera flex'. The front camera flex is one cable that organize the front camera, the microphone and also the ear speaker. So for example, you can remove the rear camera but not the front camera if you still wanna use the ear speaker. Why you wanna do this things?
Maybe it is a stupid question but you probably try different lightning cables? You can also do a hard reset, hold the lock button and the home button for 15 seconds. If those things not solve your problem you can try an another dock again. Good luck and let me know!
You probably did something wrong or the screen you buyed isn't good! If you try it by yourself you can check if the connectors are connected well. If they are, you know the screen you buyed isn't good. You can also go to a repair centre and let them check whats wrong.