Have fun at the school! He might find the noise and activity quite full on, I know Kipper did the first time I took him near a school at chucking out time

Short visits might work best for you an him, or he might LOVE the attention
With the weeing, I don't think it's a bad thing for now; if he's already regulating himself it's only going to help with building duration. If you haven't already, maybe think about introducing a word that you say in a bright, upbeat way when he does a wee - our breeder used 'puddles!' and for the first 3-4 months we had Kipper we felt prize eejits standing in the garden and happily saying 'Puddles!' every time Kipper did a wee. But man alive, it worked after a while and it's been so useful - on car journeys when you need to take him out for a quick break, before going into the vets, at dog training...the list is endless.