In quantum physics, a force can be represented as a wave or a particle (or vice versa). And, in terms of space-time, gravity is a "negative" wave, or a wave that represents attractive energy which interacts with energy & matter. Since waves can be thought of as particlesin quanta, the graviton, a gravitational wave's particle representation, is a unit of attractive force. Therefore, gravity's status as a force is preserved by quantum theory.(This is illustrated when you are accelerating, by the force you feel opposite to the direction of acceleration, relative to the frame of reference that is changing velocity relative to an outer field (note that this was said by einstein,(not by me; I don't see how this illustrates how spacetime works) though not word for word))
Answering your second question, the interaction with irregularities in space-time is the particle-particle interaction. Plain space-time has no energy, and therefore no quanta to affect matter.
Next, you are correct in assuming that space-time is the "force field" that matter interacts with to create gravity. (WARNING: PERSONAL OPINION AHEAD!!!!) I think this is due to matter being contained within space-time as a moving part of it. If it is part of space-time, it's "positive" energy would necessitate a negative counterpart; hence, gravity exists today.
The last point is because space-time includes all of those higher dimensions. This means that any higher dimensions than length, width, height, and time are also affected by gravity.
P.S. I made this answer as simple as I could while still answering the question, so please ask for any missing details.