The universe is our traditional word for everything there is, known and unknown, as you say. But language is an evolving thing that adapts to new facts and concepts. There are bigger unknowns than the unknowns conceived of by the original word “universe” if a multiverse exists. I doubt a multiverse actually exists but the concept exists. We just need to understand what words have evolved to mean today. A universe today has some limits to its meaning, until your amendment request is processed anyway.
Confusion about “space” I understand. The word “space” has two accepted meanings in cosmology. One meaning is that it is the apparently empty background in between the objects of the universe. The other meaning is that it is topological manifold in which the universe resides and includes all objects of the universe. The latter is the space that still expands or inflated when it was empty.
I don’t think “stuff moving apart in space” applies to space of either kind. This is somewhat of a metaphor for something that I can’t explain well, nor cosmologists it seems. It means the “scale factor” of the universe is changing. We are kind of measuring around some kind of growing curve rather than in an invariant straight line between faraway objects because our measurement basis includes elapsed time, that is, we are not measuring a distance in the ordinary meaning of the word “distance”. Spend some time reading about “proper distances” and “comoving distances” and then explain it to me.