One of the NSF commentators commented the fuel for the landing burn comes from the header tanks (little extra tanks for this kind of thing). Still, I would think if one of the closed up sections had a hole that it would cause all sorts of other troubles.
Yes, that is correct - they need the header tanks to make sure that fuel is immediately available, not sloshing around the main tanks as the ship flips. Rockets really don't like sucking in vapour. I'm not sure if they're pressurized separately from the main tanks though - I would assume not, as that would be more complicated, but I could be completely wrong.
The strength of the body of the rocket comes from some level of pressurisation – much like a drinks can. I suspect that if the tank got holed the ship wouldn't have held up during the flip
