I was there this March, almost the same dates you specified.
Weather was wonderful during the day, shorts and t-shirts. The evenings were a bit cooler but being from New England, I was fine with the cooler temps because they were much warmer than home.
Attendance was pretty low. I never have the occasion to use FastPass for anything other than Peter Pan's flight and this trip was no exception.
We stayed at Old Key West. The place was very quiet. I should mention that this was our college spring break trip but we didn't run into many other spring breakers. I've heard they show up a week later or two later.