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
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