We are fostering our first bengal. He was not socialized well, if at all. He comes from a chaotic household.

We are just about 3 months in and he is finally walking into other parts of our house, but still runs away if we come into the room. He lets us get with 3 feet of him to feed him. I've caught him playing with the toys we have for him. And, he and my sphynx play peek-a-book & run away. He still will not allow us to be close enough to touch him, so we give him plenty of space and just talk to him and don't act shocked we he walks into a room we're in.

My questions are:
1. How much should I be feeding him?
He comes from a raw meat household, so I started off with a high quality wet food with a dash of kibble (3oz can w/ 1 Tbsp. kibble) in the morning and raw beef for PM feeding. (was 6oz)
I have worked him off the raw meat and do 2 wet food (high meat content) cat foods (3oz) with the dash of kibble. I'm not willing to make cat food.

His coat has gone from dull to shiny, so something is working, but he also seems to be chonking up. I don't want to overfeed.

1. Any suggestions on how to best socialize him? Are normal cat toys enough stimulation? I've never had a cat that wasn't social.

2. He doesn't see any of my cat treats as food. I did find he love freeze dried chicken hearts and Churu, so he has started recognizing those words when I say them now. What other treats do your bengals enjoy?

I just really need to get him to the point where we can touch him to take him to the vet. We haven't been able to do that yet and I don't want to traumatize him further by just grabbing him and putting him in a box.