There will be no permission sought for setting up play school from all those authorities you have mentioned
The framework of fees versus the facilities must be transparent. A schedule for interaction with parents from time to time regarding academics and administration is important.
The staff whether teaching or non teaching, needs to be experienced, trained and genuinely interested in spending time with the kids.
The location for preschools / daycare / pre primary schools also matters.
A sound and quality infrastructure is important. This constitutes classrooms, play area, wash rooms, pantry and office. The space need not be very large but must be adequate and well ventilated. The interior can be simple but has to be convenient for the kids and of good quality. A colorful interior is recommended for preschools. Cleanliness, hygiene and safety are relevant and that goes without saying. The preschool market in India exhibits a lot of variation.