Unfortunately I agree with others that this is common practice.
some of it may be intentional cost-cutting measures, as running a nursery is a high-cost business to run and margins can be tight. I believe this is why so many of them often do employ very young girls, because they are cheap due to their age.
On the flip side, the 15 minutes early thing can be common in a lot of places and it just means, as a pp said, be on the premises, jacket off, bag stored, hands washed, ready to start on your starting time.
ie if the nursery opens and kids are being dropped off at 8am, your daughter can’t also be arriving at 8. She needs to be there and ready by 8.
Staying late - not sure. There should hopefully be a lot of cleaning going on, so surely not crammed into the final 15 minutes. Maybe they all stop childcare and start cleaning as soon as kids start leaving for the day and numbers allow and one person stays with the final kids and they have to be prepared for a parent being late?
I think you just need to wait and see what it’s like when she starts. You get good nurseries and bad nurseries, and I think you will be able to tell which it is based on the training she receives and how much support she gets towards the qualification.
Good nurseries hold onto and develop staff. Bad nurseries have a high turnover of young, unqualified girls.