[tromper]

For the overall problem I'd guess they the other posters are right.
That's a pretty common thing to flake on all the smaller carb'd scoots.
I have the opposite problem to a lesser extent with mine. It doesn't like to engage on warm days strangely.
To get around this I just make sure I'm solidly on the brake and "lightly" hold the throttle open while cranking. keep it a little cracked for a few seconds while vacuum establishes and the motor realizes it's alive, and good to go.