B.M.
Kindergarten is very different from pre-school, but some of the questions are pretty much the same - here are some more that I would ask, in addition to the ones from the other mamas:
*Are there are special food restrictions - is it 'peanut free'?
*Will they open items (sometimes they won't open granola bars or fruit cups)?
*Will they heat up items (soup, macaroni&cheese)?
*Do they have to ready themselves to go outside (button/zip own coat, tie own shoes), or will the teachers help?
*Do they have to put on their own clothes after going potty - ie button and zip all pants etc (if it's preschool and you are talking about a 3 year old, you need to find out if they need to be able to wipe themselves after pooping).
*Do they still nap? If your child isn't still a napper, can they just have quiet time?
*how will it be handled if your daughter is upset?
*What are the guidelines for when a child must be kept home due to illness (usually the 'gray' areas are runny noses and coughing - policies will differ)
I'm sure there are others that other mamas will think of.
Good Luck.