How winnings are reported to the IRS: Form W-2G. The payer must provide you with a Form W-2G if you win: $600 or more if the amount is at least 300 times the wager (the payer has the option to reduce the winnings by the wager)R$1,200 or more (not reduced by wager) in winnings from bingo or slot machines.
There is no limit. Casinos who bar people from playing generally do it for bad behavior. Card counters can get banned from playing certain games, but this isn't nearly as common as people like to believe, mainly because the effectiveness of card counting isn't as great as people believe.