"One modelin base contact with the gun emplacement can fire it instead of *HIS* own weapon following the normal rules for shooting".
That would be discriminatory against female models. That said, I haven't taken the time to model any genitals onto
my models, though what you get up to with your greenstuff on your own time is up to you.
I'm taking a look through, and so far as I can tell, anything that isn't terrain, that you can volutarily move around, is a model. As such, yes I believe that a Vehicle could fire a Quad-gun. If you need rationale, perhaps one of the crew hop out momentarily and squeeze off a few rounds, then hop back in.
Since the rules allow you to fire the Emplacement
instead of "his" weapon, I'd say a model couldn't fire any of their own weapons, even if they normally would be able to fire more than one. Rationale would be that any weapon he has would be "his"... so he can't fire it.
To the third question, the 40k RB, pg 71 top left says that distances are measured to the vehicle's hull, so as long as the hull was within range of your objective [Maybe your flyer was immoblized and you removed the stand, or maybe you have the objective on a tall hill or something...] it can score in missions where vehicles are allowed to score.