Check the laws in your city. Most cities have laws against discharging a firearm in the city limits, but an air rifle is not a firearm. So, in most places, you can use an air rifle any place you can't use a firearm. Cemetaries, parks, are two places that come to mind. We own Beeman pellet rifles, 5 MM, 177, and a 25 Cal. The 5 MM seems to be the best for taking anything up to and including ground hogs. If you check certain history books, you will find that it is believed Gen Patton was killed by a shot to the back of the neck from an air rifle. Most spring piston air rifles seem to hold their velocity better than the pump up air rifle, because as you pump air into the chamber on the pump up rifles, the air gets hot and expands. If you don't fire the rifle before the air cools the pressure reduces as the air cools.
I learned the hard way that a pellet gun can take out a skunk. I shot one in my back yard. I just wanted to drive it away. It just fell over, dead. Fortunately, I was in possession of a airfilter mask and a pair of ruber gloves.
Most cities treat pellet guns same as firearms. You must check your local laws
1 shot is quite right. While most (not all) pellet pistols do not put out a lot of energy (FPE), there are pellet rifles that could do serious damage to a human. I have a PCP rifle in .25 cal that can put out 50 FPE which is just 20 FPE less than a .22 short cartridge. I cannot see any advantage to carrying a pellet pistol. What would be your reason to carry one ?I have a pellet rifle that has made very accurate head squirrel shots at thirty yards using my pointed hunter pellets. I have little doubt the velocity I've seen to that range and with that pellet or the flatter ones, a head shot would kill, if not seriously impair or disable a human. Also don't forget the great distinction between pellet guns and " some'" air rifles, that are out there.