I think that's a cochin bantam mix.
the coloring might be similar, but the body shape is different
here is a picture of one of my cochin hens for comparison
city cats are usually well fed. I live out in the country and get quite a bit of feral cats that most likely were dumped. I've killed about half a dozen this year that were caught in the act of killing chickens.
but that being said I only had cats kill 1 at a time.
I've had weasels kill a...
I've had catournix live over a year around my place until predators got to them.
it's very rare for them to breed on their own. but very possible. but the main problem I see is that they are way too easy for any predator to get.
if you want her to sit on eggs you can leave her. or if you don't want chicks, then try putting her in a separate cage for a couple days to break her. I don't have much experience with making them stop being broody, I usually let them incubate the eggs.
do you have a rooster?