the first issue is familiar to me as my first laptop had this issue, while running Windows XP. the fans were going out and simply couldn’t move enough heat. the solution then that mostly worked was one of those laptop stands with fans built in. it worked most of the time, but a real solution might mean cleaning out the chassis and maybe replacing the fans.
for the second, i didn’t really have trouble setting up the Nvidia drivers just following the docs. sorry if that isn’t helpful; i’m stuck with Nvidia for my ML/CUDA stuff.