1. Losing battles will lose prestige. Researching technology, winning battles, building prestige buildings and some minister / ruler traits increase prestige.

2. The type of merchant ship doesn't matter. They all deliver the exact same amount. Fluyts & galleons are much more expensive to maintain (~300 - 350) vs Indiamen (50) and dhows, so I would recommend you use IM as your trade ships and fluyts & galleons as warships. Otherwise, you need to park them on ivory or spice to make a profit with those ships.