"Sitting perched" implies sitting on the edge of something (a chair, a table, a balcony, a ledge, etc.), the way a bird does, often with the connotation that the seated person is eager or excited. "Sitting perched on the edge of their seat" like they are excited enough that they might fly away.

Perched usually applies to birds it means to be sat high up on something narrow like the branch of a tree, or a narrow cliff face/ edge. For caged birds we supply them with man made perches to rest upon. For a person it would imply sitting on something high up and close to the edge, but this is not always the case, people do sometimes say perched when they just mean sat. Sometimes they say perched to imply either not looking comfortably or looking comfortable like a perched bird, so a lot depends on the circumstances and how it is said. you can say either "you have not forgotten it" or "not forgotten about it"

1) sit perched describes how Andy was sitting - like a bird. Other examples: he sat still, he sat straight up. 2) I would use about because you are saying that you did not forget about the request. If you say I did not forget it, you are referring to the milk. Cases: A. You have not gone to store yet: I did not forget; I did not forget about it B. You went to store: I did not forget; I did not forget the milk (here it is); I did not forget it (here it is)

The addition of 'awkwardly' does not affect the meaning of the sentence. It just accentuates the fact that the sitting is awkward, and uncomfortable, rather than being relaxed.