Will time travel become possible with a great understanding of how time works in space?

We are always travelling forward in time. We can - and already do to some extent - observe the effects of time dilation predicted by special and general relativity.

If we constructed a spacecraft that accelerated at #1g# for about #14# years (ship time) then decelerated at #1g# for about #14# years then that would be sufficient to cover the #2# million light years to Andromeda. Any surviving passengers would be #28# years older than they were when they set out, but from the perspective of observers that stayed at home, it would have taken about #2# million years for the trip (one way) and it would take at least another #2# million years before they heard back from the travellers after they had arrived.

Our current models do not support any mechanisms whereby causality is violated. Causality pretty much precludes travelling backward in time. If it were possible, then we would be faced with various paradoxes. It might be resolvable with some kind of many world interpretation involving a branching of reality. So you would only be able to travel back to a point which is not on the same branch of reality on which you started. This would not be very useful.

Note however that we can observe past events - in fact that's all we do see since the speed of light is finite. We see the sun as it was about #8# minutes ago. We see Proxima Centauri as it was about #4# years ago. We see the Andromeda galaxy as it was about #2# million years ago. We observe (with the help of our telescopes) galaxies as they were about #13.6# billion years ago.