Both concerns are serious ones, but could be handwaved with the same argument: it's a Variable Gravity Area, just like it sez in the signage.
The mass of the air within would indeed be just a tiny fraction of that needed to appreciable move the ship - unless it were given extra momentum. Just opening the door would not suffice, but opening the door and
changing the direction and strength of the artificial gravity within ought to be enough to turn the air into suitably "momentous" rocket exhaust. Remember, gravity doesn't fail when power goes out: it should be just as easily available as door-opening power.
People within should be able to hold on to the railings easily enough if the door were opened; Crusher would have to repair some popped eardrums and whole-body bruises, but nobody need die. Adding the gravity trick would mean everybody would be thrown out and die, though - unless gravity were used creatively, remaining down-pointing and ramped up near the floor but becoming out-pushing (and ramped up) a meter above the floor...
Unless they thought this was predestination paradox then separating the ship would not have been something they would have normally done during the first pass when the problem began.
True enough - but separating the ship is something they should
have been doing whenever problems like this began. Could they really be sure they wouldn't have done it this time around?