c.1300, from what + ever. Variant form whatsoever is attested earlier.
Perhaps; possibly •Often a reply to an unanswerable question, with the force of ''Could be'' or ''We'll see'': Well, whatever. The point was, he was dead/ Which I can do on my own, or whatever
[1900+; perhaps a shortening of whatever's fair, attested in 1960 student use]