How does she seem when you pick her up? Is she happy and playing? It seems that she does like school and her teacher. That would be what I would go by. Some kids have a harder time than others saying goodbye and separating. My daughter is 3 and 9 months, and has been in preschool two days a week since the end of January. She loves her teachers, loves her friends, is always upbeat and energetic and excited when I pick her up. But when it's a school morning, she drags her feet, complains, cries when I drop her off that it "takes too long" for me to come back. I try to remain matter-of-fact, and communicate that I trust the teachers and that school is a fun place, and she has grown a lot and has a much easier time. I used to watch her after I left from the observation room, and over time she would cry less and less, until now she might cling to me and complain but doesn't burst into tears like she used to.
One thing that seemed to help is when I kneeled down to her level, and told her that I know it's hard to say goodbye, I don't like it either, it's hard for me too. That seemed to calm her down, perhaps she felt that I was hearing what she was trying to say.
It sounds like your daughter might just be trying to talk about all the new things she's experiencing, and having to learn. From what you say, perhaps nap time is a hard thing to adjust to for her? They probably turn off the lights for nap time, and if it's quiet then things feel very strange. I might also talk to her teacher to find out how she's handling things, and maybe see if they have any ideas for the transition.
One thing that my daughter's teacher had us do was paste some pictures of our family onto a piece of construction paper, and put that into a sheet protector. She kept this in her cubby, and whenever she missed us she could carry that around and look at it. She loved this, and would tell her friends in class who all the different people were. We made sure that they were pictures of her with us, and her with her grandparents so that she could see that she was still part of us as a family.
Another thing that I have done is try to make a game of our drive to the school. We pretend to "eat" the trees and plants that we pass, calling them broccoli, or spinach. If we see a red car, that's our ketchup, or a yellow car is our mustard. My daughter loves this, and it distracts her enough that she doesn't get so worked up on the way. Other times we'll pretend that we're in an airplane, or that we're different cartoon characters that she loves flying along. Then again, some days she's just not into going to school!
I know how hard it is to see your child in distress, but remember that preschool is really good for kids, they get a head start on learning, and learn all about how to interact with other kids and adults. My daughter used to be really afraid of other kids at the playground, now she'll go up to them and ask them to play on her own.
Sending a hug to you, feel free to send me a message if you have any questions or just want to vent!
L.