You don't have to book any transport in advance. Tickets for the Full Moon Party and transport (taxi / speedboat / ferry's) are widely available. If you would like an accommodation close to the Full Moon Party you should book in advance. Most of the accommodations are fully booked close to the party.
Yes taxi's are driving all night from and to the Full Moon Party. Prices usually start from 100 Bath.
The most common sold drinks are buckets. Price can range from 150 bath up to 500 bath close to the beach. Be smart and walk away from the beach and safe yourself some money!
Tickets for the Full Moon Party can be acquired at the door. The price for a ticket is 100 Bath.