What carburetor are you using? The idle circuit for the carburetor is essential to run at idle/low rpm and when you let off the gas the throttle returns t idle so if there is no fuel delivery by the idle system it is just like shutting off the fuel and ability to run.
As HRL indicated choke operation for starting is important so perhaps an explanation of your starting procedure would be heldful.
I agree with the others that some water in the exhaust is normal so until you can determine if it is normal condensation or some other source concentrate on the starting/running issues.
