There is a small dance floor in the Club. It is pretty marginal for ballroom. It is underutilized so not much competition for space. Music is varied but occasional waltz, club sorts of music, etc. The dance pros who provide the evening entertainment sometimes run classes but they are very basic. Some of the deck area is opened up for dancing during particular evenings but it is crowded and definitely not very ballroomy.
WWfT, The simplest way is Welcome pickups. It can be prebooked and seems to be about the same price as a taxi. We used them a few years back and they were fine - clean, punctual, very helpful drivers. I've also done it by metro. We had the misfortune to arrive in mid taxi strike and had no other way to get to the port. The metro was fine and easy to use. Unfortunately, there is a significant walk from pireus metro stop to the cruise terminal. The walk was interesting while dragging our baggage.