Your barrel has not been shortened, as noted by the integral front sight ramp.
The stock looks like an aftermarket stock, it seems like the angle on the bottom of the grip is different.
I am not sure about the sights, but PetahW typically knows what he is talking about, so I would take him at his word.
Refinishing the gun would cost more than the gun is worth. Leave it alone and cherish it as a memento of your father.
32 Remington ammo is scarce. If you find some, grab it.
Never try to educate someone who resists knowledge at all costs.
But what do I know?