BF3 = BF:BC
and no, there's no plans as of yet to release for PC
there is nothing I can find on "BF3" alone, Bad Company is the third installment (excluding 2142/Vietnam, which are really just sort of stand-alone expansions - 2142 uses BF2's engine and Vietnam used Vietnam used 1942's engine, this is an entirely new engine, so it's safe to considered it BF
3)
sucks eh =\