The wild cat doesn't let us pet her, but she begs for food at my door and ofc I feed her

She probably used to be a house cat that was abandoned and stayed in the barn, thus becoming wild.
Many people drop their cat in the country when they are not the cute little kitten... but they have no idea that most of those cats can't survive the harsh winters in a cold barn...
That black wild one has long hair so she's ok, but how many cats died in horrible manner just cause they had owners who didn't feel like having them anymore

I ended up with 4 cats in the house but I can't take them all in

Sadly it seems to happen everywhere. It is quite common in Europe as well. The adults adopt a kitty at the beginning of the summer vacation and abandon it at the end of the season either because it grew up or simply because they don't have time to take care of it. It's hard to understand how and why some ppl could be so heartless I mean cats are playful and adorable at all ages. They are kind of like kids, a bit hyper when they are young but still have the same behaviors when they reach the adulthood. Then again a lot adults mistreat even their own flesh and blood... They are what I call filthy humans