I think it works a bit like this. Say space is a sheet of paper. It's not, but say it is. Stick a moderately heavy ball on it, and it makes a dent. This dent represents a distortion of gravity, which is affected by mass. A white dwarf has a large mass, so it forms a steeper dent. A black hole has infinite mass, so it has an infintely deep dent. However, the immense gravity of a black hole doesn't affect energy (which has no mass) and this is why black holes emit X -rays and other electromagnetic radiation as the superheated gas which surrounds a black hole breaks apart under the gravity of the black hole.
Of course, space is in 4 dimensions, so my example probably doesn't work.
Faster than light travel is technically impossible because as speed increases so does mass. Therefore, at the speed of light you have infinite mass. There are, however, several different theories how to bypass this. Wormholes are one, while Alcubierre's Drive (where space is contracted in front of a ship and expanded behind) is another idea. Hyperdrive is indeed meant to be faster-than-light, as it would be impossiible to cross the galaxy without it (which is done numerous times - Darth Mauls trip from Coruscant near the center of the galaxy to Tatooine in the Outer Rim, for example).