The leak is probably coming from the fuel overflow. So either the float setting is too high, or the float valve is stuck, dirty, or worn.
As for the choke, it gets stiff at the top. Pull it a bit further and it should "click" into place at the top. There's a spring in there so it will not stay up if it's not snapped into place at the top. If it won't click at the top then take it out and clean it, inspect it, put it back if nothing looks wrong and try again. Carb rebuild kits are generally junk. Buy the individual pieces you need from sudco, pats small engine, jets r us, etc. You can get the parts for the choke if you need them, as well as jets, float valve, gaskets, and just about anything else you would need. Most the stuff is cheap.