Be happy that it seems you have so many good schools to choose from! The school should give you a deadline to accept and register if you get chosen. Where we live, there are maybe 5 or 6 preschools that are convenient, and have good programs. They required a deposit with the application. If you did not register when you were chosen, you would lose all or most of your deposit. I believe they did this to cut down on people sending out so many applications. My advice is to go with your gut, if you get the acceptance from one of your first choices, go for it and ditch the rest...if they are all good schools, you won't know the slight differences between them once your child starts going to the one you choose!
Also, your child is 2 1/2 now, but will be 3 1/2 when she actually starts preschool....the potty training will be much further along by then or most likely completed. In my experience, the schools are very strict on the children being potty trained, if they had an accident, the school called to have you come and change/clean your child up if necessary. The school would need a different type of certificate to be "qualified" to change diapers (I think it is a daycare license vs a preschool)
I know it seems like a monumental decision, but if these schools are all so good, you will probably have a good experience at any of them, so relax a bit! If you have applied to 5 or 6 or more schools, she should get into at least one! If there is no deposit required, knock yourself out and apply to as many as you want. It sounds like there is a massive shuffle going on in your system, and there is no penality for you ditching one school if you get another offer you think is better for you. Your system sounds like a massive pain in the butt! Ours was probably not much better.... We have waiting lists and $150 deposits, so we are forced to be selective, but I don't have any friends that did not end up at some program in our community that was good (maybe not their first choice) My daughter got into her school (the only one we applied to, because we did not have deposit money to burn like some of my more wealthy neighbors!)The school had a list system and my husband sat in a parking lot at the school at 4 a.m. untill 7a.m. when they put the sign up list out! We got her on the list to definitly get a spot, but we were put on the waiting list for our first choice of classes, because alumni and their siblings get priority (she was enrolled in our second choice) We got a call in early August, that someone had moved and we got our first choice, but even if we had not, it would not have made any difference in retrospect!...it will all come out all right! Focus on enjoying how much she will blossom and grow-- no matter which school she attends. GOOD LUCK