Screen died and fixed itself a month later.

I've never seen that issue before. Usually a faded display is due to a faulty Display.

FYI, you should check to see if your laptop qualifies for the Battery Recall program.

https://support.apple.com/15-inch-macbook-pro-battery-recall

I don't know. Could be the internal screen cable. Could be that maybe you accidentally pressed some of the accessibility key combos ? who knows for sure? You could reset the smc/pmu and zap the pram which wouldn't do you any harm. how to do that can be found on Apple's support page for Notebooks. As for your computer getting extremely hot, If you're sure there's nothing covering/blocking the vents when the computer is in use, eg you're using it on a hard surface, rather than on a blanket, and you've made sure there's no dust or crud blocking the vents, and you're sorta worried, then your next step might be to book an appointment at your local Genius Bar and take it in for an evaluation. That is free. I hope you have Apple Care + for peace of mind, maybe your home owners insurance might cover something ??? anyways, make the appointment and take it in. I don't work for Apple, so my opinion is just that, and it's free too

jb