Cats are obligate carnivores, which means they NEED meat in their diet, otherwise they become malnourished over time. A cat not getting enough fatty acids such as Taurine can develop heart and eye...
Yes - just not medium rare ;o)
Make sure your meat's cooked thoroughly and you're onto a winner. They say to stay clear of Liver though... I did, but my Mum lived off liver and onions when she was...