My three small birds, a bourkes parakeet, a splendid parakeet, and a linnie, play together well and can be housed together or separately. The grasskeets sometimes bicker. They scream at one another and beak fence, but have never gone so far as to actually bite anything other than the end of a tail feather. The linnie doesn't actually stand her ground and beak fence if the boys are after her and she doesn't like it. She will retreat, but protest loudly.
The bourkes is not good about sharing food in general, so I have more than one bowl with favored food items. None of them gripes about sharing vegetables, lol.
They share most of their toys. The bourkes will not share vine balls, his designing toy. The linnie will not share her sleepy hut, but that is no problem because the grasskeets don't want to go inside it, anyway, but she had to scream at them at first to assure herself they would not try to go inside.
She is ok if they want to sit on top of it. The splendid has no toys he protects as his own exclusive property, but does enjoy teasing the others about their favorite toys just for the shear joy of irritating his friends. They are all especially good at sharing any of their hanging toys. They actually seem to enjoy playing with these together.
The bourkes and the linnie will preen one another, so I think they get along well. The two grasskeets bicker more often than the linnie bickers with either grasskeet, but never to the point where I feel one is in danger. Sometimes, when I want to sleep, I will tell them to knock it off. They always do, which is more than I can say for my sons when they were little and bickering. In fact, now that I think about it, those three birds, two males and a female, have pretty much the same relationship with one another that my kids have.
The more I think of it, the more the comparison works, lol.
The senegal, who outweighs all the other birds by nearly triple the weight, is NOT allowed physical contact. African poicephalus, and I believe most african species, do not flock with birds of other species in the wild. They have been known to kill birds they do not get on with, even birds of the same species and the opposite sex. Roni loves to talk to the other birds through the cage bars or across the room when everyone is out. I have to watch her around their cages, because she has no respect for their space and will climb on them if allowed, and I believe she would hurt them through the bars if she could reach them. She does talk to them, in bird chirps and in her few human words. She also engages in parallel play with them, and this seems to me to be a two way thing. The little birds are more often likely to follow her lead in types of parallel activities to engage in.
As for breaking up squabbles, usually "knock it off" works. If it does not, I have on occasion simply made them step up and then set them down away from the thing they were bickering about. They argue over toys and food if they are going to argue. If food is the culprit, reminding them that they have multiple offerings of the same food seems to satisfy them.