Here is how I see it as a native speaker. Someone please correct me if I'm wrong!
1. Phoebe is supposed to be kind of dumb, so some things she says might not make complete sense. The bow probably doesn't actually mean anything political. Maybe she is thinking of the way someone might wear a ribbon supporting breast cancer awareness or something like that. So it is just a joke.
2. I haven't seen that episode of Friends in particular so I don't know what he's talking about, but "Two down, one to go!" is a pretty common expression. It means you have completed two out of three things you had to do, and there is one left. He just left off the "one to go" part in this case, I guess it is implied. For example, if you had to clean three rooms, and you had finished with two of them already, you might say "Well, two down, one to go!" It usually means you are almost done with the entire thing. Also it doesn't have to be 2/3. You could say "Five down, two to go." It just signifies that you are nearing the end of the task usually. You can also use it in a joking way if you said something like "Ugh, two down, a million to go!" Just to exaggerate, if you were just starting with something.
Hope this helped! Cheers!