Can I reasonably assume the DVD players will be multi-region or region-free?
It depends entirely on the vessel, sadly.
If you want to give something to the crew to say thanks, have a chat with the Master about donating a small amount to the ships welfare fund. That way the crew can spend it on what they need most (usually a new TV for the mess room, exercise bikes for the gym, sim cards etc etc...)
Something I forgot to mention before - ALWAYS assume the ship will be a "dry" ship. Do not bring booze etc aboard. If alcohol consumption is allowed on board, you'll be able to get some from the bonded store. Same with tobacco etc.
Oh, and keep your toilet door shut, especially when showering. Steam from the shower has a nasty habit of setting the cabin fire alarm off... Which will result in some half-asleep sailor bursting through your cabin door, fire extinguisher in one hand and radio in the other screaming about a "fire"...