Your carb is probably gummed up from sitting with gas in it.I would take it all apart and soak it in gas or solvent overnight. If you use a air blower to help clean you need to watch where the float needle seats. Sometimes the seat is rubber and will blow away , sometimes they are brass and you get lucky . Try to find a thin piece of wire and run it through all the jet holes.You shouldnt have messed with the fuel/air mixture screw without knowing where it was. From screwed all the way into the carb, they usually come out 2 1/2 turns. Then its about listening to your motor to fine tune it. The rubber bowl ring you should be able to get at any lawnmower service place. Tecumseh is out of business but parts are available. If you lived closer i have a few laying around.if you run an air filter make sure its clean and not really soaked with oil or full of dirt, If you dont run one, get one. Some newer motors wont run right without them.Plus there is no point in riding off road without one and filling your freshly cleaned carb full of dirt.For the throttle sticking open, it sounds like the throttle spring has come off.if you cant find the o-ring you need for the bowl anywhere send me a pm with the engine model # and ill see what i can ship one for.