When I moved house, I had a feral living in my garden, I fed him outside, (We had a cat, she had been with us 10yrs at that time) He wasnt agressive at all, after a year I seen him out of the corner of my eye sitting in the living room doorway, the back door was open as it was warm. I fed him in the kitchen, he still kept his distance. After about 2 wks he came further into the living room. I had a cat bed and pointed to it and said get into your bed....he did!!!
I noticed he was long hairded and full of excrement and knots. I showered him (under protest, but i wasnt scratched) I even used pantene...lol
I took him to the vet, he was healthy apart from bendy legs...he lived with us for over 3 yrs. At that time, another cat started to cry up at our window and when the door opened it ran in...my hubby was adamant we are not having 3 cats. He chucked a bucket of water over her. She reappeared on the sill, soaking and shivering...he said...oh let the blooming thing in...hehehe
the first stray has died, my family cat has dissapeared..she was 16yrs old. and the soaking cat was named Clint and now lives happy with my daughter.....I get my two new furbabies on Monday and cant wait....
If your kitten is really young it might be best to try kitten milk, as she/he should really be still feeding from mother, and its great it uses the litter tray...looks like you have a new addition