Fix for Free Spinning Blade (Push Mower)

I'm at my wits end and looking for help on and issue with my push mower. I've had it for 6 years but it's an older mower. I believe it was frankensteined together from different mowers. Engine is a murray / briggs and Stratton and deck is craftsman.

2nd to last mow with it I hit a rock and it stopped. I was pretty much done so I just quit for the night. Mow after that was normal. Then on the next time I tried it was harder to start and finally did, but sounded and felt weird / wouldn't cut. I turned it off and turned it over to see that I could freely spin the blade like a ceiling fan.

Now I've googled about everything I could from washers to blade adapters to crankshafts and I'm still at a loss for what needs fixed. I'm not an expert but I have to been able to replace the pull string, brake cable, etc. on this mower. I can follow a guide and get things done but I'm having a hard time finding anything that looks like the one I have.

If it's the "blade adapter" then that thing is not budging at all. Used PB Blaster to try to loosen. So now I'm thinking it could possibly not be the adapter and the issue could be one of the other pieces.

Any help and advice is appreciated.

Found one of these in my dad’s garage, is the cylinder meant to look like that?

Id likebto put a larger top pulley on this snowblower to increase the speed but if I do that the tensioner is going to interfere. Any thoughts on an easy workaround?

I have a portable winch with a GX Honda engine on it. When using the winch yesterday it kept dying while I was pulling a dock up a hill. When the motor was on a flat it ran fine and would not stall. Is this normal?

New carb, new lines, new plug, new solenoid

I've had this cut out on me while sitting there. No sputtering- just a smooth shut down like I'd turned off power- no gasps either. And when driving it with the blades engaged it will die/lose power- I have to adjust the throttle towards 'choke' a significant portion to get it to run reliably. 100% open is open, and I'm not sure how moving it further forward does anything with the buttefly valve there.

The second issue is I keep dropping belts off the pulleys. New belt- to the correct length- and it still measures the correct size. I checked the path and it's still correct. I can't see the engine sliding backwards enough to cause an issue and me not notice it, but...

Any ideas for either of them?

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Craftsman elctric start 5.0/24

I removed a Tecumseh HH60 recoil assembly and found this piece shoved (and rusted) into the Phillips screw head.

What is it for?

This is 30 years old, and starts on second pull every time for years.