It is so nice of you to take the kitten in and give him a safe warm place

Re the runny poo, what has always worked with mine without fail is to feed only white fish, or chicken in small regular meals, then once the cat's poo becomes normal then slowly start to re introduce the usual food...but very slowly, until eventually it takes over from the fish/chicken again, I have never had to do this for more than a week before the cat is perfectly ok again.

Oh yes and he may also need worming but I would wait until his tum is settled.