(A) It certainly should. Edward Harris was a wealthy amateur naturalist and benefactor of the American bird artist John James Audubon. The two men travelled together on collecting expeditions in North America, and it was Audubon who gave the bird the name of Harris?s buzzard, after a bird collected in Louisiana. Audubon thought it was an unknown species of hawk, though it had in fact been described to science some years before from a specimen collected in Brazil.
The widespread omission of the apostrophe and the possessive is unusual, and I?m not aware of it happening with any other birds named after people. There are many examples of these, of which the most familiar in the UK are Bewick?s swan, Montagu?s harrier and Lady Amherst?s pheasant.