a free radical can be uncharged or charged - it doesn't really matter. The point is that free radicals are species that have at least one unpaired electron.
As for that atom being left over, you may be wrong, you may be right...depends. Main ones you're likely to come across: polyethylene during initiation/propagation/termination steps of LDPE production....also NO (nitrous oxide), NO2 (nitric oxide), oxygen atoms, the dissociation of benzoyl peroxides (and organic peroxides in general) which is the catalyst used in LDPE production, fluorine atoms, nitrogen atoms, hydroxyl radicals. Those are the main ones I can think of on the top of my head.