1) The two are not directly dependent in that way. General relatively can, in theory, allow for some time-travel like effects, but not ones that violate causali

1) The two are not directly dependent in that way. General relatively can, in theory, allow for some time-travel like effects, but not ones that violate causality. General relativity, and indeed most theories of physics, are actually 'time reversible', meaning they work just as well (in principle) forwards and backwards. Entropy in thermodynamics is one of the few things which directly implies there's a 'natural' direction for time. (roughly speaking, this means, that in theory, if you were to instantaneously reverse the motion of every particle in the universe, things would start to play out backwards and entropy would start to decrease. The second law of thermodynamics is basically just saying that this is would only happen if you could do it exactly. Any other configuration of the particles will result in entropy increasing) 2) It's not directly due to the forces from the gravity. In fact, it's more the other way around: spacetime is distorted by gravity and this is what produces the apparent force on objects, as well as time dilation. (or more precisely, mass and energy cause the distortion, which causes the force we call gravity and time dilation).