Yes. The gold is only protected against Brigands - a barbarian horde searches until it finds what it is looking for. So, if you don't have other resources, the barbarians will steal up to two gold from your Cache.

Yes, provided that it is your only gold.

You can accommodate your opponent's in one and the bank's gold in one other region. You could receive four gold all together as long as you have multiple regions with enough available room.

Yes, if you place Bran on a Temple, you may draw two cards from the draw stacks. In this context, it doesn't matter whether you play Bran from your hand or receive him from your opponent via the Missionary.

The number rolled with the production die applies, that is, the die is not rolled again.

The 2nd Caravel doesn't affect the trade ship. Therefore, two Caravels and one trade ship in a city only count as four units in case of a Barbarian Attack.

Yes, because the Caravel is a unit, and Traitors can steal units without further ado - as long as no special rules apply.

No, although the principality must have a city in order to be able to play the Caravel.

You may remove the Castle and build it again. This, however, will not prevent the opponent from building a Castle, because in the Theme Game a removed Castle is placed face up again.

You may remove the Church and build it again. This, however, will not prevent the opponent from building a Church, because in the Theme Game a removed Church is placed face up again.

No. On each of your turns, you may freely decide whether to downgrade a residence, but you may only downgrade one residence per turn.

You may remove the Commercial Harbor and build it again. This, however, will not prevent the opponent from building a Commercial Harbor, because in the Theme Game a removed Commercial Harbor is placed face up again.