Frogs are fine, I used to keep them in my community tank, as long as they are the small brown/grey variety and not the albino ones which become preditory when bigger. They eat bloodworm... I use to feed them frozen bloodworm. I would not keep both frogs and crabs together. Oh, and make sure your tank is escape proof as they swim up to the surface quite a lot.
There are two different aquatic frogs. I have both kinds and am quite fond of them.
African Dwarf Frogs are tiny little things and may be kept with small fish or alone in a small tank. African Clawed Frogs are their bigger relatives and tend to eat fish, even bigger fish than you would think possible.
If you click on the link in my signature, it will take you to a thread with a lot of information and links about them.
From my experience, which isn't much, crabs sometimes will attack slow bottom feeding fish. I had one that would pinch my dragonfish that just sat on the bottom.