A lot of people successfully house BPs with Africans. (Yellow Labs tend to be a popular tankmate). I personally don't think it's the best choice, but only because I think you should house New World and Old World cichlids separately.
BPs can do well with some large Americans, but it depends on the aggression level of both fish. I've heard of them doing very well with Oscars, but I wouldn't necessarily house them with a Red Devil-type aggressive fish unless they're in a LARGE tank.
Individual BPs have a range of temperaments. I have some that are absolute wusses, and others that love to pester their tankmates. The main thing with my BPs is they can't defend themselves like other cichlids can (i.e. they can't use their mouths for nipping). They can still stress peaceful fish out, though, if you have a pesterer.
I have no advice regarding Cyprinids because I've never kept them. Anybody else?