My family has raised chickens in the backyard for decades.

Getting them killed by predators isn't difficult but I wouldn't worry too much about a cat - it is unlikely to take more than one or two adults and the young chickens would likely be more secure/with an adult hen and they are quite good at keeping their young safe. Regarding malnurisment, you can literally just let the chickens walk around and eat grass, insects and whatever you throw in your compost - chickens have been eating that for centuries.

Chickens are some of the easiest animals to raise and they provide both eggs and meat. I think this is a great idea.