This would be a great power, who wouldn't want to move fast! I'm going to be a bit lucky about the physics, I think you were talking about momentum for ouch throwing (p=mv, or the relativistic version). Time travel is definitely possible, but only in the future direction, moving fast only allows you access to that direction!
A potential downside of moving that fast? Definitely Friction as you mentioned or sonic booms! You've seen what happens to deorbiting satellites and shuttles, it would be pretty hot and pretty loud!