As things stand, a pro-leave PM wouldn't have the numbers to get Article 50 through Parliament, assuming he/she went through the democratic route, unless the MPs vote in the Commons against their conscience saying 'it's the will of the people'.
I have no idea what you're on about with Labour's...
You're right, he hasn't. He was Chairman of the British Council from 2004-2009. He now sits in the House of Lords.
The only way he'd be out of a job is if the members of the unelected House of Lords suddenly became subject to elections.
It's believed 50% of Tory MPs are 'remain', 40% 'leave' and 10% fence-sitters.
A new Tory leader would almost certainly have to call an early general election as, not unlike Labour, the new leader (assuming it's a 'Leave' person, and that that will still be seen as a divisive issue) won't have...