Help identifying bass

Hi, my Grandad recently passed away and among his possessions was this P-bass I used to play when I was visiting. Here is an imgur album of the bass.

Its pretty old and beat up, but it has sentimental value to me so I intend to restore everything myself. But I don't know what bass this would be.

I'm fairly certain its not a genuine Fender P-bass. The fender logo is raised to the touch (maybe a sticker or glued on) and the area around the logo appears to discoloured or sanded down.

The precision bass logo appears to be legit to my untrained eye, and the serial number as well perhaps.

The closest guess I would have is a late 80s/early 90s Japanese or Korean (probably Korean) Squire. I haven't been able to check the electronics yet because several screws are seized, and I don't want to break anything.

Does anyone have any tips on removing these rusted screws? I intend to replace them.

Thanks to anyone who has any input on this, I would appreciate it.