I recently got 2 fire bellied toads and one young green frog, about the same size.
Can they live together? I have water with a filter, plus plants and rocks. Also some fish and a crab.

I have never had fire-bellied toads so I don't know all that much about them. I think, if eaten, they are poisonous. They also certainly may try to eat small fish. Some crabs may also try to eat fish. While green frogs are said to eat small fish, I've never seen mine do that. I have lots of green frogs of all ages so I know a lot about their behavior. I don't think they would harm the other animals but I'm not sure how the other animals would be with them. Sorry, I don't know more. I would probably keep them in separate setups just in case. I'm no expert but maybe someone else will reply for you.

I think they are toxic, I tried to let my green frog with the fire bellies and he went from jumping around to just smooshed on the glass. I would separate them.

I once had a male firebelly and a female leopard frog together, and the male firebelly would always sing to her. He actually mated with her, but she died from an injury before laying her eggs.

Well so far they are doing well, except for the crab, who has passed away.
The frogs and toads eat like crazy. They eat eveything they see. So how much a problem is overeating? Are fat toads/frogs a problem?