If it's my name for an Airbnb suite I reserved, can I check in before the other guests for my room arrive & they can just head on up once they get to the hotel?

If you're the name on the reservation, of course. The rest of them can just go straight to the room if you've already checked in. If their name is on the reservation as well, they will need to go to the check in counter and give a copy of their ID

Yes, as long as everyone name is on the reservation

Absolutely as long as your names on the reservation you can go check in and as they arrive they can just head on up once you have checked in