1) Yes, it's bribery and it almost never works, other than making your generals less susceptible to bribery, so on the whole it's a good thing.

3 and 4 are connected. Building siege weapons is a useful thing (never wondered why the AI is so hot on building them?). Catapults allow you to besiege and take a city in the same turn, wiping out the ballista/cannon towers that can wreak havoc on you. Trebuchets are the best defense against the Mongols that I've found. When they come calling, have half a dozen archer units on the walls and 2 trebuchets at your walls set on FAW and you can blow them apart defensively. Sally with a schiltrom unit activated (I think Saracen Militia for Egypt) and the Mongols will be sorely tempted, at which point the archers and trebuchets will make short work of them.