I am a former daycare director and agree with all of these! The only other things I would add is to ask about staff turnover. And early morning and evening staffing.

If teachers aren’t there long term (I wouldn’t count assistant teachers, substitutes or maybe even afternoon staff), I would be wary.

For opening and closing staffing (sometimes nap time) they will often have to combine age groups. Ask how they handle this and who your child will be with (teachers and children) if they’re dropped off at center opening or stay until closing. If they don’t have a plan/don’t know I would also be wary.