1 - Probably Baltar, or the angel version of Six manifested in physical form like in "Six Degrees of Separation" and left it. I'd say Baltar, though.
2 - I always took that as Boomer herself, at least her Cylon half. For example, she could have been sleepwalking or something, and she subconsciously put it there.
3 - Clearly Baltar's Cylon detector was ALL about finding actual Cylons. My understanding is that after Boomer's test, he modified it so everyone got "green" tests.
4 - It didn't! :-)