The Princess Fantasy Faire has three princesses that change periodically, so there is no guarantee you will get any particular princess.
Rapunzel has her own area inside Fantasyland.
We have done Ariel's Grotto twice (2009 & 2011). We got Ariel, Aurora, Belle, Cinderella and Snow White. They 'work the room' while you eat and really spend some time at each table so this is worth it if you really want one or all of those particular princesses.
I believe you can get some kind of schedule from City Hall, but we have never gotten it so I am not sure how detailed it is. For my family, it has really been a matter of luck. On our last trip, we were exiting the Space Orbiter when Ariel, Cinderella and Snow White were headed to their places around the castle. My daughter ran up to them and Ariel took her hand and ran off with my daughter. So much for all those talks about stranger danger. I was nearly running through the crowd trying to keep up with them
or at the very least, keeping sight of my daughter.
It is a favorite memory because my daughter is a real talker and she talked Ariel's ear off the entire time. And then, once Ariel got in place, my daughter was first to get her picture taken (once I caught up to them).