UPDATE: Mother cat hiding with her newborns in my wood stash
We moved the family out of the wood stash and let them find another place. They literally moved on a hollow place under the steps. We have gotten closer to the cats and now she comes by herself to get treats and pats. We feed her everyday and provide milk and water. Yesterday, we got an anti-bug oil and applied it to her. She has started putting on weight and it's nice getting closer to her and seeing her doing better.
You can get "milk" designed for cats, I bought some in the supermarket but ours was never interested. I should have asked his foster mum which brand she got him as he liked that one, but I never paid attention to the label on the carton she gave us. Oh well, it's been years now and he's fine without.