I've never had any problems with my Blood Parrots fighting. I raised them about 4-5 years ago. They can't really kill any fish pretty much because they can't close their mouths fully, and they generally are peaceful fish. So there shouldn't be any problem with them. The worst that can get for the Blood Parrots is if they are stressing the other fishes out like crazy to the point of death. That's pretty much the only bad thing they could do.
Also, if you don't have many live plants or not as much then you should put some in

Especially the Amazon Swords, since they grow very big and if you have many of them, that will pretty much keep the fishes separated. That is what I do. Although Parrots are Cichlids, so they are aggressive sometimes. Just try your best and separate them. You can't change their nature from being bad to good. Although over time they will being to be able to cope with it. I hope you know what I mean
Good luck!