I keep a Senegal bichir in my CA/SA cichlid tank and he gets along with everyone just fine. Just be sure to add the bichir after it has gained a fair amount of size, so it wont be looked at as a snack; the same can also be said for the cichlids you house with the bichir.
it depends on the cichlid. I would not try the mix with known aggressive cichlids, or breeding pairs. I've kept bichirs with oscars, severums and female convicts/HRPs.
Also, if you have some of the less active bichirs, it might be difficult to ensure they get enough to eat. you have to either stuff the cichlids, or just drop food after lights are out and hope the bichirs get enough to eat.
I have my ropefish and sen with 2 rainbows and a firemouth. Although the FM can be quite aggressive, it never shows any aggression towards the bichirs, simply because they inhabit different areas of the tank. You'll be fine.