To reek is to smell bad. So a room (hotel room) might reek of smoke, a person might reek of alcohol, an athlete might reek of sweat/perspiration, a mechanic might be wearing clothes that reek of petrol or oil, etc.

Yes, its pretty common. Along with "you smell like a distillery."

… to refer TO someone …. I learned IT from a series. You smell like alcohol. (Standard) I can smell alcohol on your breath. (Standard) You reek of booze. (More negative, more familiar) By the way, you can say ‘reek’ without ‘of something’. ‘This reeks!’ (It’s quite familiar, though)

Yes, it’s a common phrase.

Yes