Homeless or Lost?

I found this kitten (I’m not sure how old, he is FAIRLY small but he seems weaned) playing around on the streets in an area with lots of children, and all the kids were trying to catch it but it kept running away so I came up behind it and picked it up, he squirmed a bit but then he settled after a few moments. He was so skinny, his ribcage was visible and you could definitely feel how bony his haunches were. He had just a thumb tack size spot on him where the fur was missing but there was no injury there. His eyes and gums and everything else was clean and his fur was well kept. He at first didn’t seem like he liked human contact, but he became INCREDIBLY friendly after a small while and loves being held and kissed and played with. I fed him soft treats and wetted cat food so it was soft enough for his belly and some water since it was 87°F out, and he seemed content. I asked around the area if he belonged to anyone but everyone I got a hold of said “no”. So I called my local shelter and asked for my friend that works there and he said to take it home to keep it safe and put flyers with pictures all around the area I found it and wait for someone to call. When I brought him inside, he was TERRIFIED of the feeling of the rug, didn’t know how to use stairs (I have an older cat and he just copied her so he can kinda do it now but he’s still weird about it), and was so mesmerized about the feel of my comforter. So I have a few questions. One, is there anything from this that can tell me if he has had a previous owner or if he’s a stray? And if he’s had an owner, was he abused? I’m putting up flyers today, but how long should I wait before it’s clear that he doesn’t have an owner? I don’t want to get completely attached so I haven’t named him, but he’s taken on sleeping on the belly of my older cat like she’s his mother, so I’m not sure how that’s going to effect anything either. I also need to know how to set up a good flyer, I want to make sure he goes to the right owner and not someone looking for a free cat. Please help, and thank you so much in advance!