the faster one goes, the slower time moves while a fixed observer will have normal time. Not really time travel in the since a person jumps from a moment of present time to the past or future.
And it takes a lot of energy to accelerate toward the speed of light, which is theoretically impossible in “normal” space.
Sure it is. If you could run around in a circle fast enough you would find that when you stopped the clock on the wall indicates you've moved ahead in time. Problem is getting enough energy to accelerate something fast enough for the time jump to be really noticeable. Going back in the past is a completely different thing and far more difficult, if not impossible. You would need to utilize weird theorized stuff like worm holes and other such space-time manipulators.