Secondly, usually a school enrolls students in priority order. The first consideration is local hukou and nearby housing, the second consideration is housing but no hukou nearby, and the third consideration is no hukou and no housing nearby. If you open a shop nearby, you can.
However, there is a problem. If your room book doesn't come down at the beginning of school, it will be a problem and needs the developer's proof.
I am in Beijing, and I have a house but no hukou. We registered at the local public primary school, so I can go to school. But I still spent some money to go to a public primary school with good conditions a little farther away.
You can go to school to find out the situation and ask the doorman. Sometimes the school can't recruit enough people, but it depends on the school.