re: To the Moon, Alice!
I'm almost positive that the Agena didn't have nearly enough power to do that. You'd also have to seriously upgrade the heat shield on the Gemini capsule to survive a much faster reentry.
According to the Encyclopedia Astronautica, the Lunar Gemini missions would've used a Centaur upper state, a much more powerful setup than the Agena. They could've landed on the moon in 1966 for 1/20th to cost of the Apollo program. Too bad it didn't happen.