Cats are a definite mantis predator in my neighborhood. I suspect birds as well. Again, it's usually mature, winged mantises that are at the most risk, since they're a lot bolder about coming out of hiding.

Raising a mantis in a small cage can be fun, if you start with one big enough to eat easily-caught bugs. They need something to hang on properly during molting--a bad molt can often be lethal. I've watched mantises molt, and it's amazing.

Easiest way to keep mantises as pets is to catch a mature, winged mantis and keep him or her (the males have much skinnier bodies and are smaller than females). They don't molt any more, and are big enough to eat even store-bought crickets. They can be allowed to run loose in the house if nobody minds, and you don't have other pets likely to eat it.

Mantises will pinch like hell, but it takes a lot to get one to bite you. I got bit once when I was trying to feed a second insect to one that was already eating, and he simply moved a pincer to my hand and continued his feeding behavior. Never had one bite me just picking it up. Best way to pick up a mantis is to just put a hand near where it is and nudge it on. Make the mantis think you're just another bush.