I've been to one of the best party places around Mykonos - the Cavo Paradiso. The crowds really rock, and the place is going wild with shirtless men and women in bikinis. The music is also jamming too, thanks to the djs playing them. Most importantly, the Cavo's been named the 10th best club in the world.
I believe you can. Actually, since the party's to be held near a swimming pool, and there are many people swimming, you can bring your swimming trunks. No dress code of course, this isn't a formal place.