Birds can be killed with a BB gun at close range. Larger animals, such as squirrels and rabbits are not likely to be killed, but would be AT LEAST injured- which is not a good thing for a hunter- so don't try it. Pellet guns typically have more power, and SOME pellet guns are used for hunting small game.
Nerf gun
Yes
400fps can kill a bird from about 10 yards away. I have a 880 powerline daisy It will go through the bird. So ya it can
It is likely. a close range headshot would do the trick.
Yes it is passable to kill a Crow with a BB gun
You can kill rodents with a BB gun
yes i have killed possoms with a bb gun
Atticus Finch gives Jem the BB gun for Christmas in "To Kill a Mockingbird." He teaches Jem about responsibility and how to use it properly.
Depending on the power of the BB gun. They will kill most any small or medium size bird. However BB guns are not designed for hunting, Pellet guns and rifles make a better choice. BB do not deform on impact and the bird will suffer before death. Hunting with a pellet rifle is more humane. Pellets (especially hollow point pellets) mushroom on impact and make a clean kill.
Insects
BB guns are NOT for hunting. It will not kill a deer. The Answer is NO.
It is not likely, but it IS possible. Depends on the bb gun, distance, and where you are hit.