I tend to explain creature actions this way to new players. Think of each creature action as having three steps.
Step One: Activate the Creature (flip the action marker over).
Step Two: Move the creature if desired.
Step Three: Take an action. You may only take a full action if you did NOT move.
Every creature has only one action marker, including your mage. Therefore, each creature only gets to take one action on their turn, which occurs in Step Three listed above.
In addition to the action markers, your mage has a Quick Cast marker. This is NOT the same thing. The Quick Cast marker allows you to cast a single quick action spell. It doesn't do anything else. You may use the Quick Cast marker during either of the two Quick Cast Phases, or before or after ANY friendly creature's action.
You can thus use the Quick Cast marker even if you aren't taking any actions with your mage that turn. You may be using a Knight instead. However, you must use the Quick Cast marker either before or after the creature acts. You can not use it during the creature's action. For example, you can not move, Quick Cast, and then guard. You could however, move, guard, and then Quick Cast.
This has hopefully answered your first question, but if not I will be more explicit. Yes, you may use your Quick Cast marker and then take an action with your mage (Activate, Move, do a Quick Action) as you described.
As for your second question, you may choose ANY two spells you wish during the planning stage. These may both be quick action spells. They may also both be full action spells if you wish, but if you choose two full action spells you will only be able to cast one of them during the round. So it would be an either/or scenario. However, that is perfectly legal. Whatever you wish to pull out.