Welcome to Cruisemates and the world of cruising,
You actually have plenty of time to apply for a passport, most local post offices can take your application and even take a passportn pic for it...
Yes, I would read up all you can on the ports. When you book your cruise, you can book a specific cabin, so be sure to be aware of the layout of the ship and especially cabin location. Be sure to see what is above and below your cabin...