The difficulty here is is perhaps the definition of what distance and time are!
When you delve into the murky world of physics, this question becomes surprisingly elusive.
However it has become clear that, whatever they are, distance and time are both affected by the presence of Mass.
Mathematically this effect can be described by the same equations used to describe curvatures in topological problems.
Your last question is the easiest to answer, it is the Mass that causes the curvature not the volume, so a hollow Earth would not have the same gravity as our solid Earth.
