A sick bat really needs to be turned over for humane euthanasia. It's, unfortunately, really not safe for you to try and help it. While bats are an important part of our ecosystem, they are also one of the primary animals that transmit rabies. It would not be uncommon for a sick bat to test positive for rabies. Call animal control, and give it to them. If you do not have animal control, give it to the wildlife rehab people. If you've had contact with the bat, you need to tell animal control, when you turn the bat over, as they may decide they should test it for rabies. If you have had contact with the bat and it is not tested for rabies, you need to discuss this with your doctor, who may want you to undergo rabies postexposure prophylaxis.

I would suggest finding your local wildlife rehabilitator; here's a link from the humane society to illinois rehabilitators:

http://web.extension.illinois.edu/wildlife/files/WildlifeRehabbersSheet.pdf

When moving bats, use thick gloves or a towel to pick it up only if necessary (we had some confused babies get into our house, and that's how the wildlife guy removed them for us). If it isn't actually injured, make sure to put it back outside somewhere high up (like on top of a bush); bats have trouble taking off from the ground, since they more glide than fly -- if they are on the ground, they have to run a long way in order to take off.

As for what bats eat ... I think the little brown bats around here eat mosquitos, but they might eat other things, too. It might eat fruit or bugs.

I would also keep it away from any other animals and clean any areas that it is near thoroughly as they can also carry things like ringworm (which is actually a fungus, not a worm), and yes, humans can get ringworm, too.

Little brown bats have recently had issues with white nose syndrome, which I don't recall whether it's a fungus or something else, but it exhibits as white stuff on the nose of the bat, as the name implies. It does bat things to colonies, and I think it's fatal, so if the bat has white on its nose, that would be very bad and probably best to give it over the the center.