It was purportedly (and probably in actuality) intended as a survival aid to be used after landings and before recovery in the Siberian wilderness, although allegedly was intended as a defensive weapon against in-space attacks by the US space program.
Heat dissipation is an issue since there's no air around to cool the barrel, although for this three shot weapon (two shotgun one rifle) it wouldn't be a problem. This gun is mostly to fend off bears when you land in Siberia.
Yes, a shotgun could function in space. Firearms, including shotguns, rely on self-contained oxidizers in their ammunition to ignite the propellant, so they do not require atmospheric oxygen to fire.
However, the lack of air would mean there's no medium to carry the shockwave, so the gun's report would not be audible. Additionally, the recoil could cause more significant uncontrolled movement due to the lack of air resistance and gravity to stabilize the shooter. The cold temperatures in space might also affect the mechanical parts, potentially leading to jamming or other issues if the weapon isn't specially designed for such an environment.
Yes, I guess? But firing a gun inside a spacecraft would be a bad idea... and also firing it while spacewalking would be a bad idea unless you were very sure that you were very well braced & tethered.
You could load it with very small, light, or soft pellets, they don't need to be very damaging to make a hole in a suit which would be near certainly fatal.
Well, considering that many early spacecraft and space stations were running oxygen rich atmospheres, it would probably mean the end of anyone involved in a rather spectacular fireball.