Welcome to the forum.
Nice pictures.
You will want to buy a new
Mec-Gar magazine for shooting purposes.
I wouldn't worry about the grips unless then don't fit snuggly.
Download the FAQs until you can get a good luger reference book.
For WW-2 Mausers, I like
The Mauser Parabellum 1930-1946 Analysis of a Million Luger Pistols, by Don R. Hallock & Joop van de Kant