You get exactly 1 vote (to cast on others). Votes can only be cast on Random Duty players.
It's very unlikely all 8 of you are eligible to receive votes, because random duty puts you into content that is already short of people of your particular role. So at most 7 randoms and there will only be 1 vote available. Or 1 random, and 7 votes available. In the latter case, all 7 votes will either end up on that one person, or some of it won't be cast.
Nothing. We can't force people to vote either, because that would counter the whole point of the MVP system.
They're doing that as well. There will be indications on the Duty Finder that says "we're short of tanks now, queue for some bonus" kind of thing. This info is also in the very same interview with Yoshi-P.