I'm recently back from Infinity and can answer some of your questions.
There is no charge for the Thalassotherapy pool. (Thank goodness, as I used it a lot.) We had a hair dryer in the bathroom of our cabin, but there were no self-service laundry facilities. As far as room service and DVDs, we used neither, so hopefully someone will respond to those questions soon. BTW - pastries in the Cova Cafe were complimentary, but there was a charge for all drinks, including tea. (Tea was available at no charge elsewhere on the ship.)
While we went to the Eastern Caribbean on our Infinity cruise, I have been to the Mexican Riviera on another line and loved it. Which ports are you most interested in? I also suggest posting the ports question on our ports of call boards, below, for more responses.