You might want to buy a copy of "US M1Carbines, Wartime Production" by Craig Riesch. There are drawings of all versions of the parts. There is a later version of the operating slide stop (Type III) may hold the slide better, but the slide lock is never positive; this is not considered a problem, as locking the slide back was never considered important by the US military.
Based on the variable quality of CAI milsurps, plus the fact that Korean Army armorers sometimes made repairs we would consider unsafe (e.g., welding a broken bolt lug), you may want to pay a gunsmith to check it out. I'd look for a "service trained armorer". Parkerizing is strictly cosmetic, it won't tighten up your gun.
Most USGI stocks were walnut, some replacements were birch (both are hardwoods). Birch doesn't have the nice grain of walnut & doesn't take stain well, but it is stronger than walnut. Decent USGI stocks are getting hard to find out there, but there is nothing wrong with a commercial stock if made to milspec.