If space itself expanded, then is the domain of the expansion infinite nothingness?"
The universe has been measured as flat to 5 decimal places meaning, unless it begins to curve after those 5 decimal places, it is potentially infinite. I.e, i can expand for ever and not meet itself.
Now, what is it expanding into? A question without answer I'm afraid. Some guess infinite nothingness, some guess infinite space containing other universes*, some say our universe is creating its own space as it expands.
* I kind of like the idea of a multiverse. There is tentative evidence for this in the bruises on the CMB that suggest collision with other universes. And the bunches of galaxy's moving in the wrong direction away from the bruises.