Yellow stays until he gets another and is then suspended for 1 match. These cards/suspensions apply to the competition they are received. A suspended player will have no yellows for the competition he gained them in after he serves the suspension.

For reds I think its 2 yellows in a match = red card means immediate 1 game suspension. Straight red gives 2 game suspension: or at least does for actions such as deliberate handball/professional foul.