Mishhu (and their forebears) are, at the very least, capable of breathing.
There was this old RP post I read - gone now - where Wes was describing how a character could feel the 'fetid breath' coming from the Mishhu's undermaw against her face.
Considering how the Ghost Mishhu (and forebears) are capable of phasing and travelling in that state for a long time, they likely could be kind of like whales and dolphins in that they are capable of apnea to an exceptional degree. If they make sound with their maw, it needs to involve the passage of air. Considering they also have ears-like formations in their shells, it's likely they have ear canals as well (therefore, somewhat tied to breathing as well).
Mishhu (and forebears) are definitely capable of surviving in vaccuum (pressure, lack of oxygen and radiation exposure) for some length of time. That's likely also tied to their ability to survive their phased-out states.