Appears the shamrock was painted on the stock, that's easy to deal with.

Older Parkers can crack or actually split at the tang--mostly from shooting higher pressure loads. The fix for the crack in usually a bolt through the stock at or near the spot where your shamrock is located

love the art be it cover up or not..gives the gun some character...charlie

The barrels look like ejector type. I think I see a screw I the dolls head and split kickers. But it's hard to tell.
Being aftermarket barrels, the dolls head could be screwed on.

Thanks, all, for your comments! I appreciate everyone's help.

Is the extractor one piece or two pieces? Two pieces are ejectors, one piece is an extractor. Dry fire the gun with empties in it. If the shells are thrown out by a spring mechanism that clicks, they are ejectors. If the shells are just raised up for you to pick out, it is an extractor. Since the picture of the breech didn't do the trick, show us a picture of the inside of the forend. That will clear everything up.