You will only get stay credit for the room you actually occupy. So if the other rooms are for other people you are not entiteled for stay credit on their rooms. If you can get the rooms put onto your one master bill (folio) then you can get points for a maximum of two rooms. Sometimes the hotels are generous, or make mistakes, and you get points for more than two rooms.
if you are qualifying on stays, then this will only count as one stay. It does not matter how many times you check in or out, or how many individual reservation numbers you have, if you are there on consecutive nights it is considered one stay. There must be a break of at least one night for it to be considered a unique stay.