I'm not going to bother with the whole general relativity conversation here because it's all just frames of reference and I'm too tired after work, however I feel obliged to correct some factual errs.
No you can only change the speed of something. Not time its self.
Traveling near or at the speed of light supposedly slows time, however I'm not entirely comfortable with this proposition by Einstein since time isn't really manipulative, and most of it is based on observations from within specific frames of reference.
You cannot go faster than the speed of light. It is simply impossible as long as you have any mass whatsoever. Since you cannot rid yourself of mass without ridding yourself of your body, you cannot surpass that speed. The best we can do is get REALLY close.
You would theoretically need a negative mass to go faster than the speed of light, not no mass. A lack of mass such as in photons allows you to reach the speed of light. Since electrons and quarks, etc, are so tiny and nearly massless, they can reach close to the speed of light, most easily observed when they're flung from supermassive black holes.
The concept of "time" being a manipulative object is still being questioned. As far as we're concerned, particles are simply moving. Someone's going to call me out by saying that we've seen "time" change from tests, however, that's simply the slowing/speeding of specific particles. Sure, you can refer to this as time, but it, again, isn't an object that you can simply change. The theory of time travel can only apply to future preferences. We can slow down the extent of which we view something, or, slow down the particles surrounding us to a specific extent, but we will NEVER be able to reverse the flow of/recreate particles. Unless we somehow manage to build something that duplicates all particles in the universe and has the ability to restore them... but that wouldn't be travelling through time.
Ultimately, time travel's a paradox, because it's manipulating a non existent concept.
Simply to back this up, time is a dimension. A snapshot of any given moment has 3 dimensions, X Y and Z, if you will. A video has 4 dimensions, because now you associate sequence with those snapshots, and "move" through time. Hence time as the 4th dimension.
