The stocks can crack, its not unheard of, but not dead common. The U shape means that it is susceptible to cracking if compressed by over-tightening or in some cases drying out or just a general flaw in the wood, it does happen.
As for likes-dislikes of ammo it is usually due to pressure likes/dislikes of the gun. If the rifle is clean, and has a clean chamber than almost any commercial round should do, but if the loads pressure curve is far enough off from the rifles design it may choke on that specific load.
I am guessing by 'getting stuck in the action' you mean the spent brass isnt fully ejecting, or is sticking in the chamber? Either way, thats possibly a pressure issue, if normal loads work, and cause you no problems. I would suggest starting with a good cleaning, particularly the chamber, and taking it from there. There is a mod that can be done to the piston to cause it to open later, and cycle differently, but I am wondering if the issue is more closely related to other issues. Is it just not ejecting?