Granted, you had me at “This game isn't real life!”
Time is only called "fourth" because we just add it as an extra to the 3 spatial dimensions we perceive intuitively. Not because there's some specific order.
There can be an arbitrary number of special dimensions in mathematics (hence hypercubes, etc).
And according to some (quite prevalent) physics theories, there are actually more than 3 spatial dimensions in the actual reality -- string theory calculations give 10 spatial dimensions.
We could also have multi-dimension time dimensions as well. The idea of parallel universes where at least one decision is made differently from our own could instead be different dimensions of time. Move to the left or right in time and experience different choices as opposed to only going forward as I assume most of us do now. :D
If I write an equation, and graph it, it has as many dimensions as variables. Those variables might have nothing to do with time OR space.
No. Only in science fiction novels.
It'd need to be measured in meters to make sense as a real 4th dimension.