1) No, he's not running for Senate.
2) He's not "running" for consideration as V.P., that's strictly McCain's call.
3) He's already got some more speaking gigs lined up.
Speaking of Senate: U.S. Sen. Mark Pryor filed for re-election today. You can go here and click "view all candidates" to see filing so far. Only a half-day left. Action was light today. So far, about 15 House and one Senate race are shaping up for the November ballot. There are other primary contests.