First, your stock is made of Black Walnut. This stuff does not age well. And continues to dry out and shrink over the years. Thus, virtually all Parkers stocked with this wood will crack eventually with enough use. The cracks you show are not uncommon. But they are serious. You should not shoot the gun until they are
professionally repaired.
It is a gamble as to whether the original finish will need replaced in the process.
The best cracked stock fixer in the US is The Stock Doctor. He's in OR.
http://www.thestockdr.com/