If this animal is threatening any farm animals-like chickens, then it is legal to shoot them. If you are just out to shoot something for fun then no, it is illegal to shoot them.(in some states it is legal) Check your local state hunting guidelines.
Arguably no, since you can only torture a possum with a BB gun, not kill it.
possums
Possums are not blind.
Possums are eaten by snakes.
There are no possums in possum pie, as true possums are found in Australia and nearby islands, and they are protected in Australia. Possums are not the same as opossums.
Possums are mammals, and are covered with hair.
No. Sugar is not poisonous to possums.
No. Ring-tail possums are not even close to being endangered.
There is no particular name for a female possum.
Possums are not eaten in modern times. In the past, the early settlers ate possums if nothing else was available. Certainly the Australian Aborigines ate possums.
In their natural state, Australian possums are external dwellers. However, brushtail possums and ringtail possums often shelter in the roof space of suburban houses.
The predators of true possums, which live in Australia, are eagles, hawks, owls and quolls. Foxes, which have been introduced to Australia, are also predators of possums. Possums should not be confused with opossums, which live in North America, and are not related to possums.