Have a part you can't identify? Did your parts get mixed up in the shop? Curious if that chunk of metal is a part you should keep? Not sure what kind of windmill or tower you have? Post photos of the mystery object here for the community to help identify.
As far as the cylinder parts go, check close inside the cylinder on the walls. That stuff looks so old that it would be fair to say that the brass liner in it has holes . That liner is only paper thin anyway.
The plunger can be replaced by a same sized one. That one looks to be a 1 leather plunger, for shallow wells. The item on the bottom is a leather-check valve, It goes in the bottom cap, where a brass seat is pressed in. That should be the lead weight, held on the remaining leather with a small bolt.
Measure you cylinder if it's not worn out with holes in the liner, and tell me what size it is. I can maybe fix you up.
Call Dan Benjamin for parts. P M me for the phone number.
Russail if your pump doesn't have a copper liner which I don't think it does you'll want to clean the cylinder up with a drill honer just to get rid of the rust.youll need a new plunger cup and base gasket. Don't attach the cast iron duck bill to the base gasket it will be in the way replace it with a foot valve on the bottom of the pump pipe.when it comes time to hook the sucker rod from the windmill to the pitcher pump rod you have to remember the pitcher pump only has a short stroke so to take up the longer stroke from the windmill you have to put a inline compression spring to take up the longer stroke from the windmill.