C.A.
You are in a hard spot. Being a single mom to an only child makes it hard because you don't have anything to really gage against (and luckily no other parenting style to deal with *sigh*). Having my second child was what tipped me off that my oldest was autistic! I had no clue (and felt like a horrid mom).
You might be asking her too many questions. My DH's ex does this with their kid and gets him to say all sorts of confusing things. He likes school but doesn't like it. He loves her but doesn't love her. At this age they are just learning more abstract emotions such as love versus like. It is confusing to them because before it was simple concepts. Try sticking with really simple things like "How was your day?" "What things did you do?" With kids this age it is sooo easy to lead and you can ferret anything out of them - she wants to please you after all! It's totally natural.
You are the center of her universe. It's that way for kids this age. She doesn't understand the bigger concepts (like she wouldn't understand why her friends all disappeared if you moved her). I know it seems like she understands more, but that is her way of showing you she wants more control - even if she doesn't quite grasp it all the way.
Her friends are neutral - they are fun playmates. Her teacher is a figurehead - like you. If she's coping at school well her problem isn't the teacher herself, but the concept of the teacher. You go away and her teacher replaces you and she doesn't want you replaced. BUT this is something she has to learn. She has no reason to mistrust you - you have always returned! So changing to a new place wouldn't solve your problem. It might make more actually.
I wouldn't worry about the eating thing. Again DH's son (3) does this. Goes through bouts where he won't eat at his moms but comes over here and eats everything in site. Does it at school, his grandma's house....she probably is testing everything out. She wants to see the reaction. You are not doing anything wrong and neither is the daycare. She's just testing things out and the best news? She always will!
I know this is long, sorry about that, it's just we've had to deal with this ourselves. It would be one thing if she spent the entire time crying, but it's just a case of a attachment I think. Every kid has it to some degree - some more than others. Nothing wrong except it means a little more work and probably a few more tears for you! Best of luck in what you decide and remember you are doing awesome!