Time is also affected by gravity. This was proven by an experiment where two atomic clocks were synchronized exactly the same, one was put aboard a satellite and orbited around the Earth.
The orbiting clock, over a period of time, was actually ahead of the Earth-bound clock.
I’m relating this from memory, and it’s been a lot of years since I read about this, so feel free to correct me if needed.
Yes, because time is affected by acceleration, and gravity causes acceleration. So the deeper into a “gravity well” you go, the slower time passes.
This connection is one of the things that led Einstein to develop General Relativity, because he realized that if you were in a spaceship accelerating at 9.8 m/s^2, then if you dropped an object, it’s trajectory would be the same as if you dropped an object while standing on earth’s surface. So if you could not determine the difference between being in a gravity well, or on an accelerating spaceship, then he surmised that all the laws of physics should apply the same in both situations, and started looking for a solution in which that would be true.