Most likely it is a faulty digitizer (probably a weak solder joint on the flex). I would try re-seating the digitizer connector to the motherboard, just to make sure it's not loose. If you still have issues, get a replacement digitizer. If a replacement digitizer has the same problem, you should look at the digitizer socket on the board.
it's possible a connector came loose. I would take it apart, and re-seat any connectors on the inside. If the problem still exists, then proceed with an LCD replacement. You can follow this guide to get to the connectors Wii U GamePadのLCDディスプレイの交換
It is almost impossible to know the issue based on the information, as so many parts could have been compromised. I would start with getting an amp meter, so you can see if the phone is drawing any power, to try and focus in on what is causing the problem. If the phone is drawing a normal amount of power (around 1 amp), then it would point towards some kind of display issue (bad screen, bad backlight, damaged fpc connector etc), but if it's not drawing any power or minimal power, it would likely be an issue with the board.
Yes, 2 hours to do almost a full charge is normal, especially if you're using the charger that came with it. If you use an iPad charger brick, it can output 2.1amps and will charge your iPhone a bit quicker.
Take it to a more reputable repair place. Ghost touching on a screen is common with cheap screens. If you use a high quality screen, and high quality adhesive (along with good repair and frame cleaning practices), you will get a screen that doesn't lift and works like it should.
I have been reading some emails from the Chinese suppliers, that replacing the screen makes Face ID stop working. Even though the camera system is separate from the screen, Apple have made replacing the screen kill Face ID.
You can also turn off the lock/unlock feature by going to Settings - Display & Brightness - Then turn off Lock/Unlock. This should allow your sleep/wake button to work again. If you want to actually fix that feature, you will need to replace the power/volume flex as rayeasom mentioned.
Could be a short on the board. Do you know if when it was fixed, they cleaned the board with alcohol, or preferably ran it through an ultrasonic cleaner, with shields removed? If it wasn't cleaned or if the shields weren't removed, there could be corrosion.
In iOS11, it is normal for it to blank for a second during boot, it happens on every iOS 11 phone I've seen including my own phone (all original and unopened). Make sure you have upgraded to iOS 11.0.3, as it specifically says in the notes that Apple fixed an issue where the 6S would freeze when not serviced with genuine Apple parts. https://9to5mac.com/2017/10/11/ios-11-0-3/