1) Yes (or just '... we've room for one more').
- 'room' is slightly more natural for me.
2) 'If we get a full size SUV all of us can fit into it.'
3) 'Put the seats back up.'
Room or Space-
1) When there's a seat left do we say- 'hop in, we have room for one more person.'
- Or if there's some space left in the trunk do we say- 'there's still a lot of room/space left' (which one's more natural between 'space' and 'room' here?)
Fit-
2) Do we use 'fit' like this- 'If we get a full size SUV all of can fit in a single car.'
Fold up/down seat-
3) I've heard people saying 'fold down the back seats.' But do we say 'fold up the seats?' Does 'fold up' even make sense?
1) Yes (or just '... we've room for one more').
- 'room' is slightly more natural for me.
2) 'If we get a full size SUV all of us can fit into it.'
3) 'Put the seats back up.'
Fit in (adapt, be right for size) and fit into (be accomodated within an enclosed space) mean different things.
Car seats don't fold and unfold like a piece of paper.
I am not a teacher or a native speaker.
Notwithstanding the differences noted by tedmc above, BrE users would be more than happy with "How many people can you fit in it?", "How many people can you fit in your car?" and similar constructions.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.
Without any further context, I see no reason for "in a single car" at the end. I'd end with "it". The reason I haven't changed it above is because "in a single car" is grammatically correct and would work in a relevant context. Here's an example:
Helen: We need to think about car hire for our holiday in September.
Sarah: Yes, we do. There are eight of us going so we'll need at least two cars. How about a couple of VW Polos?
Helen: That's a good idea but last night I had another thought. If we got a full-size SUV, all of us could fit in a single car.
Sarah: You're right! That's a much better idea, and an SUV will probably be cheaper than two Polos.
Helen: Great. I'll do some research today.
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.