Have it checked over by a good gun smith.
No, you can not shoot anything but 12 gauge shotgun shells through a 12 gauge shotgun. Never use any ammunition other than what the firearm was designed for.
As a general rule, NO, NO, NO!!!!
Assuming it is in good condition to shoot any modern day ammo, yes.
If it's a modern .30-06 rifle, yes.
12, 16, 20, 28 gauge, or .410 bore, depending on what it is chambered for.
If you mean Taylor's & Company guns, yes.
DO NOT ATTEMPT TO SHOOT MODERN AMMUNITION IN THIS WEAPON WITHOUT HAVING IT EXAMINED BY A GOOD GUNSMITH!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Danger, Danger, Danger
You should be OK with standard loads.
Yes, you can shoot .38 ammo in a .357 firearm. The .357 firearm is designed to also shoot .38 caliber ammunition.
It is difficult to find even 10 gauge shotgun ammo today. I have my doubts if 8 gauge shotgun ammo is even made any more, but corrections welcomed.
The JC Higgins Model 583.21 shotgun is designed for 12-gauge shells, not 16-gauge. Using 16-gauge slug ammo in a 12-gauge shotgun can be dangerous, as it may not fit properly and could lead to malfunctions or injuries. Always use the correct gauge ammunition specified for your firearm to ensure safety and proper operation.
DO NOT ATTEMPT TO FIRE UNTIL EXAMINED BY A COMPETENT GUNSMITH!!!!!!!!!!!!!!!!!\ Danger, Danger, Danger