Sure sounds like earwigs!
http://www.picsearch.com/pictures/anima ... arwig.html
Earwigs eat decaying plant matter, dead bugs, aphids, and plants, especially seedlings. The little buggers especially like young melon plants, and will "skeletonize" the leaves, leaving only the hard ribs, and eating all of the leaf in between. (Ask me how I know! Grrr!) They also like artichoke plants, and will chew the central rib of the leaf- I spray the undersides of the plants with- you guessed it!- diatomaceous earth.
They like to hide in damp, dark places- under rocks, flowerpots, in leaf litter, etc. The females seem to protect their eggs and young- when I lift up rocks, I will sometimes see an earwig with a nest hollowed out of the dirt containing her eggs. I smash them all! :twisted: You can dampen newspaper or cardboard and roll it into a tube and they will hide in there. You can take the roll and shake it out for your chickens. We don't get a newspaper, so I came up with another method of control- I save beer and wine bottles, put some soybean oil and sugar (or leftover soda- coke, Dr. Pepper, etc.) into them, and place them around the garden, lying on their sides- the earwigs crawl in to feed and drown in the oil. They also like soy sauce, so you can add that to the traps too. I usually put the mouth of the bottle against a stem so they have easy access. When my traps get full, I feed the "marinated earwigs" to the chickens. Waste not, want not!
They will bite, but their pincers are just for "show". I have handled a lot of earwigs in my time, and never been bitten, but Colliepup got bitten recently! I doubt they would bite the rabbits though.