On top of that how do I see or choose who to put on it..Im never seeing the choice
I don't know the answer to jrdbrr's question, but you get the option to choose which pop to put on when you create the ship. If there's only one possible pop that you could put on at the time, you won't get anything. (So if you only have pop's with identical ethos, or a bunch of robots, you won't get anything at all.)
Under what circumstances do embassies decay? I would assume as soon as you remove the embassy, but in my ~20 hours so far I haven't seen the embassy diplo bonus decrease at all. (This might be a bug.)