Hey tykenfitz, does that engine have an electric start, or an alternator of some kind? I found an engine very similar to that several weeks ago and it seems to have some kind of motor attached directly to the crankshaft. It's missing the pull start though and something else which I didn't know what it was. Looking at your engine though, I think I figured it out! I really wanted to get it cleaned up and running, it's missing a few parts.
If you have enough slack, you could probably just cut off the broken piece and re-attach it.
A float carb is a type of carb that has a small float inside of it. I'm not too sure what all they do but I believe it has something to do with fuel regulation.

I need to learn more about them myself.