I'm just wondering if anyone knows the time the ferry leaves.
Here is the timetable for November 2011 (see orange and blue dots):
You should check in at least 45 minutes before departure. Here is a lot of information in English:
Can I buy my ticket for the ferry on the day when I turn up at Hakata port?
I think it is possible, unless the boat is booked out. I recommend to make reservations, which are possible via the internet in English (see above link).
I'm mainly using cash for my trip and don't want to go through the hassles of an internet or phone booking using a credit card.
Hassle? I don't think it is going to be a hassle. I think the potential hassle of not being able to board the boat would cause much more hassle. It is not completely unusual that boats get booked out.
Can I take my own food and drinks on board?
I see no reasons why not. In addition there is a kiosk on board.
I'm from Australia, will I need to get a visa for Korea?