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Bad idea IMO. Africans in general do not welcome other fish. They tolerate other africans, mainly because they're the only ones that'll stand their ground. A bichir is just going to turn in to a snack for them.
What kind of bichir is it? That's actually pretty important. Ornate bichir will outgrow the cichlids and will eat them. Senegal will stay decently small but that may make him a target for the cichlids.
Some bichirs are found in the rift lakes. The water chemistry is not an issue, especially if you are not adding a bunch of salt and buffer.
I have kept them together many times without any issues. If you have a little 3" bichir in with full grown open water haps or a 24" bichir in with shell dwelling Tanganyikans then yes, you will have problems. As with any two fish if one fits in the other's mouth it will probably end up there. Bichirs learn quickly where the food is and will be happy to make sure they get their share. They should be fine together.
I won't get into the salt discussion again but I know that I haven't heard of too many people keeping them together. I think it would be best for a cichlid tank and a tank for the bichir himself. Cuz let's be honest. Bichirs are awesome.
Also you gotta think about their diets. Malawi like their veggies with a few worms here or there but for the most part you don't want proteins in their diets. Bichirs on the other hand enjoy their protein. If you can hand feed the bichir to ensure that the malawis aren't getting excess protein you should be straight. But with excess protein the infamous bloat can arise.
It's a 6ft tank 500 liters not sure what birchir it is to be honest a will get a picture up soon the malawis I have a yellow labs firefish some dolphins