Ah I see.

public here means that
a) schools cannot refuse pupils for discriminatory reasons
b) schools get a certain amount of money per student to pay for teachers, materials, ...

In return for the money, schools have to fulfill some educational criteria. Other than that, schools are free.
Whether prayer is done in school depends on the school.
We used to pray before lunch, and at the end of each trimester we had to attend mass.

Though the school cannot force people to pray or to go to communion of course (freedom of religion), there is no law to prevent the school from doing this. After all, if you don't want to send your kids to a school that does this, then simply send them to another school.
As an aside: even catholic schools allow the parents to choose if their kids follow the course on religion or the one about morals (non religious equivalent).