As many as it takes to win. Last year Syracuse and UConn went into 6 overtimes during the Big East Tournament.
NBA overtime periods are 5 minutes
As far as college and NBA is concerned, there is no limit as to the number of overtimes that can be played before determining a winner of the game.
How many college basketball teams played in 1939
There are many college basketball polls. The main ones are. AP USA Today RPI Coaches Poll
13 scholarship players but no limit on walk ons