Ok...the first thing is that the lever you are talking about moving appears to be the governor arm,which it would be normal for it to move with bad idle.I really didn't like the looks of the fuel filter and fuel line.I'd change fuel filter(be sure you get one made for a non fuel pump engine) and the fuel line.I don't like the way it loops down then back up.Try to keep the fuel running downhill.Check the air filter for being dirty.After that I would get it running and try adjusting out the carb.I'd also check the carb mounting gasket by spraying some wd 40 or something while it's running.Oh yeah,might as well put a plug in it.After that...I'd say the carb needs to come off and cleaned and kit-ed.That would be what I would do.Hope that helps.jc