"Fall" into place. Very good.
So, here's the thing. There is an extremely powerful theory that treats space and time as dimensions, and gravity as a result of the geometry of space-time. The theory has been repeatedly tested and makes very accurate predictions.
I'm not quite sure what your (rather vague) description adds to that.
I'm not sure what that means. Neither space nor gravity are going anywhere.
Gravity is how we perceive curved space-time. Matter (more accurately, mass) can cause this curvature, as can energy.
Space and time are equal components of space-time. They might both be emergent from some lower-level theory of quantum gravity, but currently they seem to be, pretty much, on an equal footing.