If a player already has a yellow card, but is then awarded a direct red card (not a second yellow card), does the first yellow card still stand? The player misses the next match, but in the following match, is the yellow card still valid or is it cancelled?
This depends entirely on the competition rules, but for FIFA sanctioned competitions (such as the World Cup), the following from page 17 of the FIFA Disciplinary Code applies:
If a player is guilty of serious unsporting behaviour as defined in Law 12 of the Laws of the Game and is sent off (direct red card), any other caution he has previously received in the same match is upheld.
Most football associations will follow FIFA's lead and adopt this regulation.