Feral cat?

Can you keep it from running in the house? It's obviously semi-feral: "...an originally domesticated cat that has reverted to the wild and is no longer owned or kept by someone. Semi-feral cats may continue to live in proximity to humans and may be accustomed to their presence."

a feral cat won't let you pet it or corner it in any way, but it will allow some proximity if it is hungry enough. i have never been able to get one into an enclosed space, and in my attempts to pet them they usually arent just shy but assertive and can bite or scratch quickly if touched or attempted to touch. kittens must be socialized to humans within the first month or so in order for human contact to be acceptable and it is a lifelong preference if the cat has the loving mentality toward humans that ferals dont develop.
I had a feral acquaintance once that had kittens. i took the kittens once they were weaned and the momma cat attacked me and was very concerned, but i was able to socialize the kittens and found homes for every one of them, but momma was feral and no amount of socializing would change her.
aside from having a long one-sided relationship where the cat is obviously not going to allow you to get too near it, the only way to tell if it is socialized but skittish is if it has a chip from a previous owner that proves it was once a pet, or if it develops a desire for you to touch it. i would treat all cats as feral though because even once socialized kitties can learn to prefer lack of humans, and even though they may actually let you touch them will not allow themselves to be re-tamed totally and may actually lke not dealing with humans. all cats have different personalities in certain ways so that some just dont like too much human contact, even if they were socialized with humans at an early age.
I have taken in stray abandoned kitties too and they are just totally different from dealing with ferals. i would say that a feral could be bold kitty and come into the house for food, but if the cat is giving you the attention when coming in it could be a stray.
another thing, the cat eating dog food is really bad for the cat. dog food causes crystals to form in the kitty kidneys and could lead to renal failure. plus most dog food has too many non protein ingredients that are not good for cats. dog food is really bad for cats and should be controlled as well as you can or your new friend could be sick before you can determine if it is a friendly kitty or a feral moocher.

If it's coming into your house, it's a dumped stray and not a feral. Feral cats are wild animals, and won't willingly come into your home. Poor cat has found herself a good deal ;)

How does it get into your house?

Get cat. Skin cat, take hide to fur buyer. Feral cats have thicker skin than house cats. So they pay more for the hide. Sure way to know is price of hide.

I think if the cat were feral, it wouldn't dare venture inside your home for fear of becoming trapped.

Sounds more likely that the cat is lost or stray. It might be worthing checking local lost-cat sites to see if anyone has reported a similar looking cat missing.

Could he be someone's greedy pet? Research has shown that in the U.K. many pet cats prefer to steal other cats food than hunt for a meal.

It must be feral, or runaway, or stray. Either way, it's nice of you to take care of it.

Btw it doesn't have a collar and is black with one white spot on it's chest.