Yes, it absolutely does, so long as there is no category error, and there is none here. The Universe is just an inconceivably large, curved hole with a tiny little bit of stuff in it.

> 2) Space is not spacetime.

Einstein and I disagree with you. Prior to Einstein's work, space and time were independent dimensions. But over 100 years ago Einstein showed that relativity of motion mathematically combines space and time into one, spacetime. For all intents and purposes, anyone talking about space today under any circumstances is also talking about spacetime, whether time is specifically mentioned or not, it is always there along with space.