I would say it is one of these problems: 1.) The rippon cable for the screen is loose or damaged 2.) The LCD is damaged Most likely the ribbon cable as if the LCD was broken it would have a blotchy ink look, but I could be wrong. If opening it and examing the cable/reseating it doesn't help then you'll need a new LCD. To be honest with you if you highly doubtful yourself with the repair the iPhone 4 is pretty cheap to get fixed at most places. I don't want you to break your phone (more).
I've seen this before on a few different devices, it's always been the ribbon cable connecting the screen, you may need to replace the cable or the screen entirely if they're connected. The ribbon cable is, most likely, damaged.
- Try cleaning out the charging port with compressed air, it may be dirty. - Try making sure the charging port works, test it on another phone or buy another. - Your port may be broken, it may need to be replaced.
Honestly, man, between you, me, and the internet. Use anything that won't melt under the heat of the phone. I wouldn't use a glue stick, it might melt in the phone if it gets hot. Use electrical or regular scotch tape. I see companies use tape all the time, it won't hurt it.
Just saying it should be easy to replace, I'd assume it's almost an identical process to the s6 and s7, however, be careful, if it's only 4 days old you should definitely still have a warranty. Best buy even covers the first 30 days if you got it there. I haven't seen any replacement parts for the s8 yet, and be careful trying to seal it. You may not still have waterproofing. Try claiming the warranty.
Check with reviews for the device, see if other people have the problem. I'd say it's just a cheap touchscreen, as most touchscreen printers I've had don't have great touchscreens, but make sure no one else is having the problem before looking at repairs.
It sounds like something inside is loose such as the antenna, which could be something you could easily get fixed at a local repair shop or maybe make a warranty claim on if you still have a warranty. Make sure your phone model is made for your cell carrier (or it's unlocked) as I know many people with signal problems who use cell phones on the wrong carriers.
It sounds like a problem with the lens of the camera. Make sure that: A.) There isn't anything on it, such as film of scratches. B.) The lens cover isn't cracked. C.) Try focussing the camera a few time and see what it does, if the camera is make a very loud noise when focusing it could be damaged.