The fibers are strong in both tension and compression (not equally so, see figure 1: http://home.iitk.ac.in/~mohite/axial_compressive.pdf), but in compression their aspect ratio is very very very large so they buckle instantly… unless you glue them together so each strand is supporting the ones near it and the effective aspect ratio is much less. Aside from fiber wound pressure bottles just about any real world composite structure will experience bending forces which will put the top in compression and the bottom in tension. The designer might need to reinforce the compressive side more, depending on the application (e.g. if designing for stiffness the strength might end up with considerable margin for both tension and compression).
Probably not pressurized much in the scale of things.
Humans are incompatible with nearly every gas at 13000feet/400 atm and beyond. Nobody has done it.
Cabin pressurization might get you to ~50atm, but that's around the extreme limit, so regardless of cabin pressurization the hull has to handle most of it.
Here's hoping it has and they can be found quickly.
With a pressure differential of 399 atmospheres I don't think that the vessel being pressurized is going to be much of a factor. It might as well be vacuum.
