Question: Who was "Nimrod"?
Answer: Nimrod's actual identity was never revealed in the series. It was only known that he was a British intelligence agent. Nimrod was not Colonel Klink. Hogan had only implied it was him as a ruse to get Klink returned as camp commandant, not wanting him replaced by someone more competent who would impede the Heroes war activities. (As another contributor previously posted, the term "nimrod" is slang for a nerdy, doofus type of person, though it's unclear why that was his code name).
Question: What exactly is the "cooler"?
Answer: It's a solitary cell. Steve McQueen, star of 'The Great Escape' is known as the 'Cooler King'.
Answer: It's a slang term for an isolated jail cell. In wartime, POWs who attempted to escape or otherwise thwart their captors might be punished with solitary confinement, often in a cramped, poorly ventilated, windowless space.
Question: What season and episode was it when they had to lean the guard tower and the POWs in the camp leaned so the guards would not notice?
Answer: 1-24: How to Cook a German Goose by Radar.
Question: Why do they use gas lamps in the tunnels when they have electricity?
Answer: They would need to have access to a large amount of electrical wiring, lights, and other supplies to rig a usable lighting system. Using electricity could also drain power from the rest of the camp, alerting the Germans that something is going on.
Answer: The core POWs regularly escaped the prison camp but they made it their mission to conduct espionage and commit sabotage in the surrounding German territory. They also collaborated with different underground resistance groups and used a network of secret tunnels to help prisoners from other POW camps to escape, who then relayed vital information back to the Allied forces. Hogan and his men maintained the illusion that Stalag 13 had never had any prisoners escape in order to avoid their covert operations being shut down. Being that the prison camp is set in Germany during WWII, there were no American embassies.
raywest
Hogan has mentioned to different characters that they are actually stationed at Stalag 13 to help allied soldiers and prisoners from other Stalags to escape Germany.