There are lots of things we don't know, and almost certainly never will.
It's (theoretically) possible to travel 'faster-than-time' in to the future - accelerate a ship to >99% c, and the tau factor causes time to run more slowly. Ten years pass on board, while millenia pass on Earth. The crew could return to a totally different planet.
But to the past? No, I don't think this will ever be possible. Too many unanswerable questions, and everything we DO know says nope...
As for parallel realities- theoretically, maybe. Will we ever be able to detect anything which lies outside 'our reality'? Again, no. Because it's not in our reality.
Paradoxes whichever way you look!