Number 1 - The ball must leave the penalty area to be in play, so if the ball does not leave the penalty area but goes into the net, then the goal cannot stand and it must be retaken. However if the ball leaves the penalty area, comes back and the goalkeeper saves it, then it must be an indirect free kick to the other team as the goalkeeper is not allowed to touch the ball twice once the ball is in play and it hasn't been touched by another player.
Number 2 - If a player commits more than one offence at the same time, the referee can only punish the more serious offence e.g a yellow card offence vs. a red card offence. However if the player commits an offence and has received his sanction, nothing is stopping the referee administering another sanction if the player does something stupid within the next few seconds.
Number 3 - Yes, if you commit an offence which denies an obvious goal scoring opportunity but then put the ball in the net. The referee (hopefully) will apply the advantage law. There can still be a yellow card if the player committed the offence deliberately or in a reckless manner if it was a foul, or it meets any other criteria for the ref to deem it unsporting behaviour.