If an adult gives permission for children under 18 to see an R rated movie can the children go by themselves?

Speaking to the manager should not be sufficient, under 17 should be accompanied by 18 or over.

No. They have to be accompanied by a parent or legal Guardian. The movie theatre could get fined if they allow it.

I'm pretty sure minors have to be accompanied by an adult when it's rated R. To be sure, I suggest you speak to a manager.

No law prohibits it.

Only if they speak with manager personally