I have read that the "ordinary human's" ability to determine whether an injured animal is going to survive or not is not very good. So one should really think before killing, but if the animal is in horrible pains, the best option is of course putting an end to its misery. (I don't think it matters what Buddha is thought to have said on the subject, although I'd think letting a being suffer unnecessarily cannot be a good thing in the view of Buddhism.)
And yes, cats should be kept indoors and walked outside. If they have enough "entertainment", like people or other cats playing with them, they don't have to use their hunter instinct on birds or other animals. And a bell in the cat's neck is a good idea, it warns the potential "victims".
"and I stand
upon a mountain
made of weak and useless men"