Is #5 Foundation and Earth? It sounds like the end of the Foundation series (I don't really remember that series after the first few books, but I do remember visiting a robot on the moon). Could also be Old Man's War with some stretching to fit.

#6 (the good gods have left, the evil gods remain and normal people have to defeat them) is a pretty common background for books. A Fire Upon the Deep fits. So does the Godslayer duology (which I'd recommend to almost anyone who would read your lj).

I'm clearly firing in the dark here.