You're right about the painting being wrong on the Gemini capsule. The Gemini pilot, not the commander, was the one who did the spacewalks. The commanders were actually briefed on jettisoning the spacewalker's body if he couldn't get back inside the capsule. It was a very tight fit and there was no way the Gemini could survive reentry if the hatch wasn't closed.

BTW: no hot-shot test pilot could stand to be called a "co-pilot" so that's why they were called the commander and pilot. The same applied to the Apollo missions. The LM pilot almost never touched the flight controls. The only one that I know who ever got to fly a LM was Bean on Apollo 12 while the LM was in radio blackout behind the moon. Pete Conrad let him try out the controls as a gift to a friend. Conrad was one hell of a guy.

You're also right about the missing LM ladder. At the time, they were thinking of having the astronaut slide down a rope. Sure, it would've been lighter than a ladder but could you imagine having to climb back up the rope after hours on the lunar surface? The astronauts vetoed that idea pretty quick.

As to only having one astronaut on the surface, that actually happened on most flights. For example, on Apollo 11 Armstrong was on the lunar surface alone for some time before Aldrin joined him. I'm pretty sure that happened on every mission.