Can't change the title of a thread. Maybe a mod can do that, but it's usually best to start a new thread for a new topic. That way you will get more views and thus more help.
Also, I'd recommend re-reading what you write at least once before posting it. I'm not trying to be a dick here, I'm trying to help you get the most help you can. That ^ is really hard to understand unless you read it several times over. Most people won't have the patience for that.
Here's a good video to watch:
http://www.youtube.com/watch?v=FSHkKZArN-Y
It gives a good breakdown of how the engine is assembled.
That being said, the "throttle arm" you're referring to is actually the clutch arm. And it should not come out like that. I'm going to assume it's broken or possibly installed wrong. (Most likely broken though)
The fuel shutoff valve is broken, so you'll need to order a new one. You may get lucky at a small engine shop, but that's unlikely. So it's not "just a fuel line" like the guy said.
Now, for something temporary, you may be able to get a threaded barb fitting from a hardware store or auto parts store to use, but you will NEED to get a shutoff valve in that line. Otherwise, you can flood the carb and spill fuel everywhere overnight.
Change the spark plug too. There are several replacement spark plugs available at auto parts stores.
Good luck! I doubt it'll take much to get it running right, and it does sound like you got a decent deal on it.