I suggest that you get a popularized treatment of Special relativity from your local library; this will answer most of your questions about relative velocities, etc. Typically, one begins with the Special theory, and then uses a hefty dose of handwaving to give the student a wiff of the General theory. This never works very well, so don't be surprised if none of it makes much sense.

(Handwaving follows

In practice, the time and space coordinates used in general relativity don't correspond to quantities measurable by an observer actually immersed in the system being modelled. An example of this is the "radius" in the solution for a gravity field around a spherical object--e.g., a star. Even when it does--the "universal time" in the solution for the cosmos in the large--it may not be compatible with the spirit of special relativity, where non-co-moving observers have always different "times". What does it mean when a earth-based observer and one orbiting a distant quasar, speeding away from us close to the speed of light, share a common time co-ordinate? This conundrum can make understanding relative velocities in the context of General Relativity counterintuitive, to put it mildly.