S.H.
Sounds nice (quick and easy). No point in inviting everyone even if they were all well behaved. I think inviting a certain number is up to you.
I always thought build a bear was expensive. Are you buying each child a bear to create? That is really nice.
I think so there is no confusion (most people think they are free to leave after the cake/candles) I would let people know no food is allowed at the location, but you plan to do cake at school.