Adding fish to an existing tank containing one, two or three angelfish is generally not advisable. Sometimes, removing the angelfish, re-arranging the tank, and then adding all angels together can help, sometimes not. As you have three, I would either remove the one being picked on and leave the breeding pair, or leave the three together. I certainly would not add any others now that a breeding pair is present; they will almost assuredly not take kindly to new angelfish entering "their" space, even though they may tolerate the one they have grown up with. And as for this third, removing or leaving it is something you have to decide based on the interactions. The stronger the rejection by the pair, the more stress to the third, and this is not kind to the fish and it will almost certainly suffer and likely die.
As for the tetra, yes, they should be in a group. But before you add more of this species, I would reconsider. The Black Skirt or Black Widow, Gymnocorymbus ternetzi, is not a good tankmate for sedate fish, as Akasha mentions. Here again different fish within the species may not adhere to the "norm" but one should assume they will, and this species is a fin nipper with sedate fish present. So I would reconsider re-homing the lone fish and selecting another species. The Rosy Tetra, Roberti Tetra, and some others in Hyphessobrycon are better choices with angelfish.
Byron.