Relativity is an equation, a mathematical approximation used for calculations, and cannot be trusted as an accurate description or definition of reality. There is no dimension such as time. we do not "move" through "time". Changes in the composition an location and trajectory of objects in three dimensional space occur.
"Time" is an illusion created by memory and mathematics (physics). We can remember or calculate the past state of the universe, and we can estimate the future state of the universe (The trajectory of an object in motion, for example). There is no evidence to support the idea that time exists as a dimension. It is merely a factor. A measurement used to compare the rates of change in various objects and substances within the universe.
Also, though I am not well versed in the details of relativity, I am under the impression that the theory refers to spacetime, not space and time, and that Einstein himself considered time --as some people think they know it-- to be an illusion.
(this is not to say that time "travel" is entirely impossible either. But it is mostly impossible. Although time is not a traversable dimension, it is a physical phenomenon. Time is all of the ongoing change within the universe. if someone could find a way to reverse all of that change, even in a local area, that would count as time travel. but reversing all of the chemical, energetic, compositional, and trajectorial changes at once, even in a small space, with 100% accuracy, seems like an insurmountable task, and would likely be fairly dangerous if it could somehow be accomplished)
[also, I am aware that I am possibly contradicting myself by stating that time cannot be considered a dimension, while also stating that time manipulation is possible. I guess it could be considered a dimension if we ever develop the technology to time travel, but time cannot be considered a naturally occurring dimension, as we'd really just be manipulating space and the contents within it, or in other words, we'd be manipulating three dimensions at once, and in a very substantial way, which would create the illusion of a dimension of time]
As for dimensions, I cannot imagine four dimensional space --if it exists-- could work in the same way as the first three dimensions. As I said before, three dimensions cover all possible spatial directions. The only way that I can imagine more dimensions is using probability, multiple realities, and maybe Schrodinger's cat. That is, I can imagine that reality may branch of into multiple possibilities, and possibly a near infinite number of realities. These multiple realities would make up the points which, when connected, could make up higher dimensions.
there are some videos on youtube which sort of demonstrate this concept.
and
Other realities may naturally exist alongside our own, or may only be possibilities that could theoretically be created. Even if these other realities do exist, there would be no easy way to access them. though personally, I don't believe that they can naturally exist, and I think that the only way to create or traverse them would be time manipulation. But even then, I'm not sure that a universe could be made to split into two distinct realities existing simultaneously.
For example, if I created a spacetime manipulation device, which could effectively reverse all processes within the universe, while isolating myself and the device from these changes, I would simply be changing the state of the universe around me. a new timeline would be created, but the old timeline simply would never have occurred. The only evidence that the old timeline existed would be myself and the device. This is because I have not traveled through a dimension known as time, I have simply manipulated the state of the universe around me, while leaving myself and my device unchanged.
If there were two of these devices, and both were used at the same time, at different rates or directions ("foreward" or "backwards"), well, I don't have enough information to accurately predict the results, but I can guess that either one or both devices would break (likely creating an explosion or explosions of unimaginable magnitude), or the universe would rip itself apart. The latter could possibly create a new universe or multiple universes, but there would be little to no continuity of the old universe. These would be brand new(ish) universes, so there would be no branching of our original timeline.
Now, if I happen to be wrong, and multiple universes can or do exist simultaneously, and can be traversed, then I imagine that higher dimensional life would evolve from beings who initially learned to travel between different realities, then began to exist simultaneously in multiple realities, and then to exist as an amalgamated entity with components of itself located in several different realities, the way our cells are located in different 3d locations in our body, and that these entities could be the links that create higher dimensional structures. That is how I imagine higher dimensional structures and objects could come to form.
I'm fairly positive that two dimensional life is not possible; that life needs at least three dimensions to exist. This is because life is the result of an interaction of chemicals and compounds, atoms and molecules, etc. None of these things exist on a two dimensional level. In fact, as far as I know, nothing exists or can exist on a two dimensional level. Even the things that we perceive as two dimensional, such as drawings, are actually 3 dimensional.