Very shy/emotional girl. Not sure what to do

Hey Ladies!
I need some advice. I have a 2.5 yog and she is extremely shy and cries at a drop of a dime. She has been with me for 1day/wk and has now moved to 3days/wk and eventually will be full time in September. She really is a good girl and super sweet. She is finally starting to come out of her shell a bit and is starting to talk a bit more and yesterday she actually started to follow some of the other kids around. The majority of the time she just plays on her own, doesn't say much and is most happiest when the TV is on (which is really only on while I get lunch ready and for like 15 min after lunch while everyone is getting ready for nap time - bum changes, teeth brushing, potty, etc).
She cries when she is unsure of things for instance she cries when we are singing songs (almost like she is upset that she doesn't know the words), she cries EVERYTIME lunch is coming - as soon as she gets in her chair she starts to well up and then stops when the plate is in front of her. She is a VERY picky eater so some (actually most) days she just sits there and won't eat anything. If I ask her to start eating she starts to cry. I always try to serve one thing that I know for sure she will eat but truthfully that isn't a whole lot and I refuse to make different lunches for everyone because all of the girls are picky eaters (There are 3 of them). When I lay her down for nap or if she knows nap is coming she cries like it's the end of the world. So I normally have to sit in the same room as her until she falls asleep. Eventually this will have to stop because I can't sit with everyone.
I have no idea what else to do with her. She really is a great girl. She listens well and is overall normally happy minus these key parts of the day. I'm hoping that when she starts to come more throughout the week she will cry less but until then I have no idea how to help her.
Any tips or suggestions would be great.
Thanks in advance

I think moving to 3 times a week, and then ESPECIALLY when she is full time you will see a major change. When she learns to anticipate exactly what is going to come next she won't stress about the transitions during the day. As for eating, just serve it and let it be. If she doesn't eat, she will be hungry and she will eventually learn that is the repercussion of not eating. Certain temperaments take longer to adjust, and then with her only attending 1 day/week it hasn't really allowed her to transition fully. I think you'll see the biggest change when she moves to full time!