Does the fan sound like it's functioning properly or is it grinding? The fans speeding up are normal since your CPU is being used more when those apps and games are being used. When plugged in most laptops have higher power modes they run in that also cause the CPU to ramp up. I would do the following. (1) If you are not comfortable doing the few steps below take it to a reputable repair shop. (2) Remove the fans and heatsink from the laptop. (3) Blow out the fans and heatsink fins with an air compressor if one is available. If not, use compressed air away from the laptop so any accidental condensation doesnt get onto your motherboard. (4) Remove and replace the thermal paste with something like Artic Silver 5. There are tutorials on YT on how to do so properly. Opinions will vary. Under heavy load, your laptop fans will still kick on and make noise. That's what they are designed to do, however, a good cleaning and thermal paste replacement will keep the temps down. This may keep the fans off or less noisy...

That is definitely LCD damage. Damage like this can be caused by pressure such as when it's in a back pack. The only fix is to replace the LCD, which in this case it fused to the glass/digitizer. Unless you or a local shop as the tools and skill to separate the glass from the LCD, I would just replace the entire part.

This one can be tricky because you dont want to force anything causing damage. Do you have access to a proper sim eject tool? I know a paper clip should and will work, however, I have had this very issue you are explaining. Worst case scenario is that you will need to remove the back and reset the sim eject pin. It's a black plastic pin near the sim tray that looks like a tiny cylinder.

More than likely, yes, a screen replacement will fix this issue.

It appears youll need an MSATA to USB converter. Amazon.com: SABRENT USB 3.0 mSATA II or III/5GBp/s SSD Enclosure Adapter [Support UASP (EC-UKMS) : Everything Else|new_window=true]

Water damage is tricky. It's hard to tell if you will have residual issues from a "repaired" water damaged device. However, in your case, just focusing on the issue at hand, I would bet replacing the display would fix the issue. Now, there is a chance that someone else is shorted causing no display but, in my experience I have "fixed" device by replacing displays after water damage.

No, the only way you can do so is by either knowing the email address and password tied to the phone or owning the phone itself and being able to show Apple ownership for them to then remove the iCloud lock.

Yes, any lines in the display itself on any product are from the screen itself almost all the time.

Frequent kernel panics due to thermalmonitord, missing sensors: TG0B - iPad Air 2 Wi-Fi - iFixit

Is your battery swollen? Have you tried a different parts supplier? Lastly, are you using the screen only repair or the one with the screen and frame?