1: That is odd. Tavern bedroom chests should be the same as any other, which means I usually find items in there - mostly medical stuff, occasionally something else. I've never found money in a chest.
2: Don't try to sail directly into the wind. Depending on what type of ship you have (and whether you've fitted the "Stay Sails" upgrade) you may be able to sail at an angle into the wind, e.g. if the wind is blowing from S then you may be able to sail SE or SW, but not even a ship with pure fore/aft sails can sail S, straight into the wind. Instead, you have to tack. Try to furl your sails so that you have none set as you pass through S, then set them again as you swing round to SW or SE. (Watch the other ships, you may see them doing the same thing.)
3: Get better swords and put them in your weapons locker, which you'll find by going from port to your ship deck, then to your cabin. Your boarders will take whatever weapons you put in the weapons locker, starting with the best, and any crew who survive the battle will put them back. You can also put armour in the weapons locker and the crew will use that, too.