Can a kohen serve as chazzan for mussaf on days when there is birchas kohanim? If so, what is the proper procedure for him to follow?
If I'm reading Shulchan Aruch 128:20, 22, 25, with Mishna B'rura, correctly, the rule is as follows. But contact your local, orthodox rabbi for any practical cases.
Is the shatz (leader, "chazan") the only kohen, or are there others?
In all cases, someone not a kohen should prompt the kohanim and say "kohanim" (though not "elokenu..."); however, if no one present is able to who's not a kohen then the shatz should prompt the kohanim and say the introduction, unless he's doing birkas kohanim.
The Sephardic mesora is that the Sha"tz who is a Kohen covers his eyes and stays silent for the duration of the prayer, as he is essentially taking himself out of the room. Then a non-Kohen calls out "Kohanim!" and leads the entire Birkat Kohanim.
I am not sure what happens when the sha"tz is the ONLY Kohen in the room. He probably says the "Barekhenu baBerakha..." as the Ashkenazim do.