1. AA guns are the only way.
2. No. Your planes may not land in a territory in the same turn that you capture it.
3. There is no maximum. If you run out of dice, just roll them again.
4. You’re right, it’s not legal. All combat movement must be completed before any combats are resolved. The only exception is offloading land units for an amphibious assault if a sea battle must be fought first.
5. No. Units that moved in the combat move phase or participated in combat may not move in the noncombat move phase. However, the Panzerblitz National Advantage allows German tanks to do exactly that, but only if all of the defending units are wiped out in the first combat round.