If a football player A fouls player B in a manner such that they will receive a yellow card, but the referee plays the advantage rule, and subsequently player A fouls another player, can the referee give him two yellow cards, and hence a red card, one for each foul, or does player A get only the one yellow?
Yes. If both the offences deserve a yellow card each, the referee is obligated to show the player two yellows (and hence a red card). The referee must indicate that the first yellow is for the first offence and the subsequent yellow for the second offence.
After the second offence, the referee must stop play immediately unless there is a clear goal scoring opportunity. Advantage may not be played on sending-off offences unless a clear goal scoring opportunity is present.
See FIFA Laws of the Game 2015/16 page 73
Yes it is possible and it happened in the Euro 2016 qualification play-off between Northern Ireland and Hungary in September 2015. A video of the incident is available.
Yes, if the referee deems the offending player's actions as cautionable. A list of all cautionable offences can be found under IFAB Law 12 - Fouls and Misconduct, 3. Disciplinary Action.
The Law also explains about offences temporarily waived due to an advantage:
If the referee plays the advantage for an offence for which a caution / send off would have been issued had play been stopped, this caution / send off must be issued when the ball is next out of play, except when the denial of an obvious goal-scoring opportunity results in a goal the player is cautioned for unsporting behaviour.
That means a player can receive 2 yellow cards if they commit a first cautionable offence and continue to deny an obvious goal-scoring opportunity (which ends the advantage).
That being said:
Advantage should not be applied in situations involving serious foul play, violent conduct or a second cautionable offence unless there is a clear opportunity to score a goal. The referee must send off the player when the ball is next out of play but if the player plays the ball or challenges/interferes with an opponent, the referee will stop play, send off the player and restart with an indirect free kick.