OH this is a super interesting question and like. dreams have always been crazy for me even before I was a system (like both as a kid and before I was aware) so my experiences probably aren't at all similar to other systems at all. but I wanna talk about it anyway so!

for me, I've rarely ever been "myself" when I dream. and this can take the form of either being someone non-specific or being a character or person that is explicitly not me. I've had dreams where I'm a cis guy or cis girl or even a trans woman a few times and very rarely are my dreams connected to actual things happening in my life. when they are then I'm usually more myself! but a lot of the time it's a plot from a movie or a game or something. and we share memories so we all remember these dreams when we wake up, and our dreams are as vivid as memories (which leads to some disorientation, but our memories aren't clear anyway so we never mistake dreams for reality when we're awake. it's more so a problem for the rare times we have a dream that makes sense and is congruent with reality because we can be genuinely unsure if it was a memory or dream. and we can read in our dreams too? so usually it's just something nonsensical happening that proves to us it wasn't real).

since properly opening up as a system and letting others front more though we've had dreams where we've been specific members! there was one dream I know where we were louie and another where we were hale, and the hale one was particularly weird because he dreamed about walking with another system member? and feeling that person present as separate from himself is like. it was a really nice part of the dream but so strange.

headspace wise we honestly don't really like exist in the headspace the way I think a lot of systems view themselves as doing. we rarely have memories of being in the headspace, it's just a visualisation tool for us. so like I wouldn't say anyone ever leaves the headspace even when dreaming and that we just stay there if we don't? if we don't we don't, there's just sort of nothing. and I don't think we've ever been inside the headspace during dreams either, but I know of systems who frequently do! it depends on the system I guess!!

but yeah dreams have always been weird as shit for me and I probably have a sleep disorder but I have work tomorrow (not actually) so I can't think about that rn.

oh yeah but some people. even if they weren't the "person" in the dream? feel more connected to it when we wake up. like we had a nightmare once that clearly wasn't nerve but he was the one freaked out about it yeah. this is a rambly answer and if it doesn't make sense to you yeah me neither anon!!