Sounds like you need a carbie rebuild, if they've shat themselves you wont have a hope in hell of getting the thing to run right.
Sounds like your starter is on the way out.
And yes, the light means low oil pressure.
"the reason that the idle is high, is because the battery is charging" yep, crack smokers. If anything, a charging alternator is going to drop your idle as its putting more load on the motor.