yes
yes it's in the same parking lot as Budget but on a diff. floor. If you walked, then you probably came into Treminal 1. If you come into 2, 3, or 4 it can be quite a walk, it's much easier to take the three minute ride on the free shuttle (leaves every ten or fifteen minutes from between the terminals).
Now back to the topic- went to FLL last night and there was not one car in the ES and only one G6 in the EA. Everyone was going crazy. I waited 7 minutes till they brought up a few cars and picked Prius Hybrid.