Some times they eat cats
cute dogs, cats, and other animals
That's true. It's been an issue near me as well. Thankfully in the most built up parts of London the foxes seems to mostly have enough food to not be particularly interested in cats. But I always keep an eye out when I see the cats here get close to foxes in case it turns nasty (not happened so far).
"No! Spit it out! Bad fox!"
Odd to see the fox "indoors" and domestic, and cat more "bush". They're both problematic invasive species here, but cats are mostly domestic, foxes wild/feral. Would make an interesting pet, I am guessing.
The foxes are still more shy here for the most part. They'll run if I open the door or if they see me move too much inside, while the cats will sometimes come to me and some of them (that one in particular) will come inside. But the gazebo is too tempting for both cats and foxes when I'm not out there.