How to care for little lost Kitten?

My Brother's friend hit a kitten with her car a few nights ago. It wasn't hurt, it just bumped it's head. She brought it here for the night untill she could take it to a no-kill center but my brother accidently let it loose outside.

Well, tonight it was outside on top of the hose crying. It didn't want to come in untill it saw my cat, Bootsie. Anyway, I let him on the back pourch with my cat. Bootsie isn't too bad with him, but it worries me a little. He hisses at him if he gets too close, and growls too. He tried to bat him once (he's declawed though) and charges at him once and a while to try to scare him I think.

I have no idea how old he is but he is tiny as can be with huge eyes. He's been eating solid food just fine though, so he's not too young.

Now to my questions, he is eating and drionking the stuff that I gave him with no problums so that should be fine right? I think it's purina cat chow, maybe kitten but I don't think so. Will Bootsie be ok with him? I don't think he could hurt him much, but I mean health wise. I wasn't thinking when I let the kitten in and now I'm a little worried that he could give Bootsie a desise or something. Also, the kitten coughs once in a while. He's practically inhailing his food so might it be that? I'm not sure if we'll take him to a shelter or not, I'm pretty fond of him myself. I'll get some flea and tick meds from the store tomorrow put on him and Bootsie just in case. Anything I should know? He's nice as can be to me, but still a little timid, I'm pretty sure he was wild too. Sorry this is so long.

P.S. What is the difference between play fighting and real fighting in cats because I just looked out at them and they are chasing each other and charging at each other, but no real biting or scratching.

Yes he can give your other cat a disease..You should keep them seperated until he goes to a vet and gets a checkup, vaccinations, etc..
As far as his coughing, possibly an upper respiratory infection, which is common in strays, shelters, etc..
They might just be playing, but keep in mind the major way to pass disease is biting, and scratching..

Can you see if there is a low cost vet to take him to tomorrow??

My mom wouldn't let me take him to a vet, she doesn't want to keep him. I think he might have been a pet, he's really friendly. I think he likes me too, he comes right up to me now. He's not really coughing much anymore. I think that they were just playing. They're out there now playing...tag.

maybe you could take him to a rescue or humane society.

We are either going to try to find his owners, find him a home with a friend, or take him to a no-kill center nearby.