We've recently discovered that there are at least two other cats in the building, which could be why we saw a flurry of mouse activity before we got ours.
I have just discovered that our cat likes icecream. As regards chasing mice he is a pacifist. The other day he was seen lying in our garden with a dormouse nibbling a fallen apple about 30cm from his nose.
My cat presented me with a very much alive and wriggling mouse yesterday. It was a great big ferocious critter, probably weighing well over a quarter of an ounce.
Well, I managed to catch it, then popped it in a cardboard box for an hour or so to give it a chance to calm down, then let it go, ready for the cat to catch at some other time.