Trust me; it's different when it's your own kid (or at least, it's supposed to be if the hormones are working properly). Although I babysat extensively as a teenager, I sometimes had to restrain myself from strangling the little monsters! But after I had my own, I found myself cooing and babbling at my baby (that's the magic of oxytocin). It becomes habit - I can tolerate other people's kids MUCH better since having my own. And my kid has become a young adult, unstrangled.
Kids who torture critters should be (mentally) tortured themselves, if they are old enough to understand that they are being cruel. If they aren't old enough, keep the critters safe and out of sight of the tyke.
As for crying, I found that pretending to take great glee in watching a tantrum can shut it off. They sulk, but hey, they aren't screaming anymore! I didn't even have to do it with my own kid - a friend did the pointing and laughing. He was furious but, from then on, he only cried when he was actually hurt. For the crying from minor injuries, a kiss and a band-aid work wonders. For a middle sized injury, a candy works well, if only to get the little mouth doing something other than producing noise. For major injuries, call a parent and take the kid to the ER!