Most ships have computers in varies parts of the ship although on the whole near to their computer class rooms as you can register to do certain courses.Some have wireless access so if you take a laptop with you and register and pay it is not free you can do it this way but best to check to see if the cruise ship you are booked with has this facility either via their brochure or via their internet site.
Depending on Which ship you are on there are internet cafes or computers that you can borrow. I have recently been on Royal Caribbean, NCL, Fred Olsen and MSC and all of these had internet access.
Yes but computer time is expensiv.
Island star and island escape have internet dont know how much to use.