As play is continuing you hear a lot of shouting and turn around to see two players from the same team fighting each other. After you have stopped play what action if any do you take against the two players and how do you restart the game?
Don't be fooled by the fact that the players are on the same team, that is irrelevant here. Both players are guilty of violent conduct so you must show them each a red card and dismiss both players.
Because you stopped play to issue a card the restart is an indirect free kick to the opponents where the fight took place.
Take a look at this video to see such an example
While the ball is out of play for a throw, a defender strikes an opponent inside the penalty area. You dismiss the defender. Do you restart play with a) a penalty, b) a throw or c) a drop ball? Explain your answer?
Because the ball was not in play at the time of the offense then you must restart the game the same way that you would have had the offense had not occurred. In this case that's a throw so b) is the correct answer
With play just outside the penalty area you see a defender swing a
right hook at an attacker. The attacker sees it coming so ducks out of
the way? Both players are standing inside the penalty area. Do you stop play? If so what action would you take against the
defender and how would you restart the game ?
Yes you should stop play. The fact that the defender was unable to land his punch does not let him off. He is guilty of violent conduct and you must show him a red card and dismiss him. Because the offense took place in the defenders penalty area restart with a penalty kick to the attacking team.