My daughter studies K2, not so much homework. It's ok for a 4 year old kid.
No need to worry about the admission. If you think or feel like the school, just go and try.
I applied the school because of the environment. I know nothing about the school. Even when it came to the interview, i just let my kid talk to the teacher and that's all. She was happy when she had a lot of gifts after the interview. I think the most important thing is your kid feels 'comfortable' when staying with a stranger , that is the teacher. I saw some kids crying when they had to leave their parent to have the interview.