Is that the insignia of the Hansa on it's sail?
You could say so. There was a white and red pennant. Many hanseatic cities display a red and white cross pattée in their flags:
Longboat: I'd suggest clearing a few black pixels from beneath its bow to remove the last hint of a ram. Maybe brighten the shields on its side so that they can clearly be seen.
Quinquireme There's not a lot of room in the image, but I'm thinking that it would look cool if you could put one of the castles that were on the old Cog onto this ship, it would look more like a "Floating Fortress". Maybe also decrease the size of the main sail so that the ship looks proportionally larger.
Consider it done next time.