entirely depends upon situation and location. usually unacceptable within city limits, recreationally at least.
Real property or personal property?
as long as it has an orange tip but no shooting person without glasses.
It depends on where your backyard is. If it's your backyard and you are in a rural area, you should be OK. But if you are in a less rural area, there may be laws against discharging projectile weapons like BB guns, arrows, and paintball guns.
Common law
Property, Family, and Personal Injury Law
By law, 18 to buy, under 18 you can be supervised by an adult to use them. But it is illegal for someone under 18 to take the marker off the premises without an adult. :)
The law of the state in which the property is located, for real property, or for personal property, the law of the owner's residence.
Check your local laws for a solid answer, but typicaly shooting your gun on private property is fine.
Every state has its own laws regarding what to do with personal property of an evicted tenant. You'll need to check with your state's rules.
It depends on where you are. In must U.S. states, there is no registration. Guns generally fall under the same laws as other property in a divorce, so it depends on what the local laws are about dividing property.
You will have to check your local laws defining and governing the disposition of abandoned property.
Get a copy of the all the laws relating to firearms of all the states you will be going through.