1) You do not need a ship every square. Sea trade is automatically handled by the computer. Each city has between 1-3 sea trade routes. Each turn, it will trade with the X most profitable cities it is capable of trading with. That can change depending on wars, blockades, and pirate fleets as well as trade rights.

2) When a new pope is elected, the pope-o-meter changes. The faction from whom the new pope came gets the greatest boost. The pope has a tendency to favor his home faction also, though that isn't automatic.

3) To cause problems for the various factions, no other reason. You can either spend money on building and maintaining a navy, or you can save that money and live with the pirates. The choice is yours.

4) Not really. There is a list that shows which cities are eligible to be a crusade target when you request one. No city off the list can be chosen.

5) This number varies. The size of the garrison results in a positive modifier to public order. It can't go higher than 80%, which requires a very numerous garrison to population ratio. Total public order is a sum of a bunch of modifiers in both directions. The larger the city, the more troops you need. You have to adjust this one on the fly during the game.

6) Yes/no/maybe. The AI betrays alliances a lot. It's better about it if you have a good reputation, a strong military, and are well liked by the faction in question, they are less likely to betray you.

7) The Pope Monster™ does occasionally show up. It's normally when the Pope winds up with more territory than just Rome, either because someone gifted land to the Papal State or because one of the neighboring factions went to war with the Pope and lost territory to him.