I'm still learning the ropes, but from what I've seen:
Award stays don't count for promotions or for elite nights.
Stays that are partially cash and partially award stays count as a paid stay, and the cash nights count as paid nights.
I don't think the currency matters.
Any consecutive nights in the same hotel, even if they're on separate reservations, only counts as a single stay.
Timeshare stays by owners using their ownership or exchanges do not count (although they do count for elite nights).
Nights earned from things other than stays (rollover nights, CC annual nights, CC spending) don't count as "paid stays" but do count towards elite nights.
Hopefully someone will be able to add more.