I am assuming they are calling it a school but are actually licensed through the child care licensing agency for care that is more than the regular hours of a school associated with a school system/district such as Head Start. Due to the fact that you stated it is licensed. Schools do not get licensed. They are a school through the local school district and the teachers are employed by the state or through a private school fund if it's a private school.
They must have that income information to qualify for reimbursement for their groceries. They show they have a diverse group of families, they must be able to prove they feed 100% fruit juice, that their foods are healthy and good quality, and that they are providing good eating skills to the kids they are caring for. If they don't have the income verification they are asking for they could possible lose their contract with the agency they work with to get the reimbursement funds from. They also get extra money to pay staff to prepare the food and clean up after eating. It benefits them a great deal to gather this information. It is not something lightly treated, it is a great deal of money to them.
All children under Kindergarten age are REQUIRED to nap, if they just do not nap the are REQUIRED by the state, no matter where your child is staying through the day when you are not with them, they are required to at least rest during the time they have naps scheduled. The state regulations are not going to be ignored or not adhered to. Your child should be given quiet things to do AFTER the other children have dropped off, she needs to be quiet during this time so she won't wake the napping children up. It is a long time, I agree, it seems forever to a child. But her alternative is to lay down and try to fall asleep.
I have a 4 yr. old that will not go to sleep. He started being sent home after lunch because he thought it would be fun to run from his teacher and bounce on his sleeping friends heads to wake them up. Those other kids deserved to get their rest so I am glad to go get him so they can rest.
For 4 yr old children the regular class ratio for children to a teacher is 15 4 yr. olds. The age of the teacher makes no difference, and actually a younger teacher has much more energy in the afternoon than an older teacher. They play more with the kids, have more patience, will be able to problem solve better, etc...I always hired after school high school kids to take the late afternoon kids. It was just way more fun for the kids.
An actual school age child, at least 5 years old and enrolled full time in Kindergarten has a teacher child ratio of 20 kids to 1 teacher. So if your child will be in Kindergarten next year they will have even more kids per teacher.
It really sounds like you have an exceptional care giver facility for your child, whether they call themselves a school or child care, they are going by the STATE required rules and are trying to do the right things by your child.
As for them having someone come in and observe your child, schools are required to do this if they have any behaviors that seem to fit the criteria for possible issues that will effect the child's education. If the child has some sort of diagnosis from this observation and eventual more in depth interaction then the school will form a team of people who interact with the child and with the parents will write up an Individual Education Plan or and IEP that will be formatted to help this child reach the highest level of potential this child has. They are required to pay for the evaluations, the work with the student, and the staff to fulfill any special needs the child may have. But chances are they won't find anything at this age.