1) Yes, the whole base loads at once. A few seconds of demorecord is all you need.
2) I'm not sure about this one, since intra-base teleports weren't a thing on live and I only ever used demorecord to make base records. My suspicion would be that it doesn't, since you've already loaded the entire base when you first entered.
3) Unfortunately, I can't answer this with certainty. Items in storage should be saved along with all the rest of the base's data but I don't have any way to actually verify that it does so.