Fighter aircraft cockpits are pressurized, otherwise you wouldn't be able to breath even with an oxygen mask. When you breathe out you need the external pressure on your chest to force the air from your lungs. For a short period you can breath with less pressure with low efficiency - which is why you need a richer source of air ie. higher oxygen content, in an airliner emergency mask.
The mask on a fighter pilots helmet is also to provide convenient place to put communications gear and to provide an air supply if the cockpit failed or you had to eject. This does lead to another problem, if you have to eject at high altitude you suffer a rapid loss in pressure - this is equivalent to ascending from underwater too quickly and pilots can get the bends. This is the justification for the airforce having a diving research facility.
Flying at very high altitude aircraft (eg an SR71 or U2) the outside pressure would be too low to allow you to breathe, even with an oxygen mask. This and the high temperature and high speed of the airstream if you had to eject means the crew had to wear pressurized suits.
How long the plane could remain flying would depend on the nature of the damage, there is nothing particular special about supersonic on a small scale - there are still numerous openings, intakes, ports and other holes in supersonic aircraft.
The canopies are pretty strong - bullet proof is generally a user requirement - so they wouldn't shatter on impact. There have been pilots killed by canopy failures or accidental ejections but there are also pilots who have survived the disintegration of an SR71 at mach 3