Question: When Conan is learning how to use a sword, why did the teacher slap Conan in the face and then kick the other student in the chest?
Answer: Like an Army Drill Sargent, he was berating them for not doing it better. Toughening them to become the best they could be.
Also, the other student laughs at Conan's punishment, so the teacher kicks him to teach him some humility.
Answer: Not in the movies, but in the original books. He escaped by grinding his chain between two millstones until it broke.
Twotall