I think the answer is
THE GODFATHER or, if you prefer, VITO CORLEONE.
The number of brains found inside Ron Paul's head.
ONE, unless this is a most regrettable intrusion of politics into PSE. Or maybe "brains" here can mean hemispheres, in which case there are twice as many?!
With playing or model; it rhymes with small bread.
ROLE (which rhymes with ROLL).
A half of the seats of one-seven-two filled.
Dunno. Just SIXTY-SIX? I haven't found any super-plausible thing for "one-seven-two" to be a reference to. (Planes, cars, trains, all possible.) [EDITED to add:] Most likely, as suggested by Eutherpy, is that 172 means the Cessna 172 light aircraft, in which case the number would be TWO -- which, see below, is certainly the number we want.
With character, lead, voice; between screen and guild.
ACTOR or perhaps ACTORS.
In best-of-three, rounds that one needs for a win.
A breathing gas followed by claw marks on skin.
Notable breathing gases are air, oxygen, nitrox, heliox, hydrox, hydreliox, neox, trimix, heliair. Claw marks on skin: scratches, welts. No combination of these seems much use to me, with or without replacements like nitrox -> NO. [EDITED to add:] Shahriar Mahmud Sajid found what is clearly the right answer, namely O+SCARS -> OSCARS.
Putting these together we get
ONE ROLE TWO ACTORS TWO OSCARS.
Therefore the character is
THE GODFATHER or VITO CORLEONE, for playing whom both Marlon Brando and Robert De Niro won Oscars. Lots of other roles have had multiple Oscar nominations for different actors, but I think this is the only one with two actual Oscar awards.
Credit where it's due:
Shahriar Mahmud Sajid got OSCAR(S), which I consider the trickiest thing here. Eutherpy got two TWOs, one of which I had had independently and the other of which I had multiple options for. Go upvote both of their answers if you like mine.