How can I say STOP ASKING ME SO MANY QUESTIONS FOR NO REASON?!?! without sounding mean?

unless you sit down and talk to her about this, it will continue. You are answering her question repeatedly . You are not giving her any clue some of these questions are inappropriate or that asking them repeatedly is not acceptable. You have allowed this to continue.
You need to go over why you are there and what your job is. It is not to dissect their home life or to question their parents motives. Her job is to assist. Also the children should not be hearing her talk about them this way. It will make it way back to the parents.

You need to take charge of her, just the way you do the student in your class. To the point where you may need to tell her to stop. Stop what you are doing, look directly at her... side you have asked me that five times today, as you have every day since you have been here. The answers have not changed. You need to stop. You are becoming a distraction and I want you to stop talking about the children in front of them.

She has been there theee months and should of settled into her job by now. You need to set boundaries. She keeps doing this because you allow her to.

We had a gal at work similar to this. Nothing worked except to be very direct. We told her she repeatedly asks the same questions and we give her the same answe every time. We asked if she had a problem remembering and encouraged her to take notes. We told her we were more than happy to assist her, but asking the same questions over and over again was getting distracting. Unfortunately it kept going on. Our boss finally would say we have already answered that move on.

I think your assistant is really caring for the children. At the same time, she don't have the confidence that she can do well that's why she ask you. I think, in her mind, she thinks that you care for those children as much as she does, she wouldn't even know you feel annoyed. And maybe the reason she is keep asking is because those problems that she found out are still there. Just like a child wasn't talking, and he still isn't talking, that's why your assistant is worried.

Actually I think she is good at preschool work, because for example when a child isn't talking, some parents wouldn't even bother to care. And who would care about that if preschool teacher isn't sensitive enough to important things?

Treat her like a student. Look back at your training and understand that she is eager to learn. She is clearly looking up to you and wants to learn. Since she is there to help you just give her things to keep her busy. Treat her like a kid and say "I could use your help today. Could you please . . . " then give her something to do across the room or something to keep her so focused she isn't near you asking things nonstop. Once she settles into her job the questions should stop.

You need to learn patients.