On your first question, yes, a fox will positively kill a house cat, and they do it quite a bit.
On the 22 magnum pistol question...
I've actually used my Single-Six for foxes on occasion. I'll admit, that it's not the easiest gun for use on a calling stand, but I have killed a few with it. It'll work fine on a chest shot if you keep the range reasonably short. I prefer 30 yards or less myself for this situation.
I think you'll have a better chance of a quick kill if you'll load it up with CCI TNT HPs. They pack a little more thump than any others I've hunted with.