Half a brain? I think you can live with less than 100% of your brain- people have survived accidents and can function with parts missing. Each part of your brain controls a unique body or mental function though so I’m sure it depends which parts of the brain remain in your head! Here is a link to a map of the brain:
Yes you can, but not as well as someone with a full brain obviously. I’ve heard of a case of a woman who was completely missing her cerebellum, at the back of the brain and may contain up to half of the brain cells. Yet she graduated from school, married and with a kid, nothing uneventful at all! She isn’t completely unaffected though, but its a surprise she can even move. Never underestimate the power of the mind!