Impossible to answer without more details.
You don't need the Form 4473 unless you are purchasing it from a FFL holder.
No
There is no requirement or provision to register a shotgun in PA
Gun registration is regulated by state. There is no federal gun registry, yet. You have to check with your state's gun laws.
As long as the serial number is on the gun and can be ran, you should be able to register it. If the number is bad, the police may confiscate it.
No
There is no requirement and no provision to register ordinary rifles, shotguns or handguns in Ohio. When buying a gun from a dealer, the dealer makes a record of the purchase on a Form 4473, which they keep at the shop.
Yes. The gun powder is contained in the shot shell.
You need a lawyer.
No
Depends on how old Montana is.
You need to register it in Alaska even though your father let you borrow a gun until you can get one.