Use a Pellet gun or rifle. Pellets deform on impact and make a clean kill. BB do not deform and are a poor choice for hunting. Use Hollow point pellets for hunting.
Depending on where you live and the local law. Yes a pellet gun will kill a squirrel. I suggest you use "Hollow point" hunting pellets.
No. A pellet gun would use compressed air.
Use C02 to propell the pellet
No. Even if it would fit in the chamber, there is no firing pin on a pellet gun.
Nope. Pellet guns are fairly safe to use.
I think you mean pellet gun. That is a gun that fires a small lead pellet but does not use gun powder. It uses compressed air or compressed gasses to push the pellet.
No
Use a .177 cleaning rod and push the pellet back out of the loading port.
the proper size
It can't use a regular cartridge, no.
Yes it does.
I assume you are asking about air guns, if so then it would be helpful if you stated the model. Most air guns can accept all weights of pellet grains as long as the pellet is the correct caliber. In other words you can not use a .22 pellet in a .177 caliber pellet gun but you can use different weight pellets as long as they are .177 for that gun.