Question: Why and who were the guys following Rocky in the car when he was training?
Chosen answer: People who worked for the Soviet government assigned to spy on Rocky.
Question: How did Santa, Anya, Donner and Blitzen get to the North Pole if they passed out?
Answer: They were magically transported there.
Answer: They were Rocky's chaperones. They were even seen in the cabin Rocky was staying in and playing chess with Duke.