Looks like its time to give it a good look over...meaning looking all over it...sounds like carb problems to me. And old fuel is only contributing to da problem. If the needle and seat has a rubber tip, its probly crap. The accelerator pump sounds like its not working either. And i there are any rubber fuel lines spliced in, i bet the inside of em are disintegrating. See the common denominator, Bad fuel and rubber dont get along. Double check all secondary ignition, and if and when its all good. Dig into the fuel issue. If you have a ,"known good carb," drain crappy fuel, service lines as necessary, and try it. Dont over look a failing fuel pump either...Food for thought.. keep us posted. And good luck.
