Let's start from the beginning.
Which screw is broken? A sprocket cover screw? The screw that fits into the brass cable end? The nut that threads onto the tip of the clutch release cam (sticks out on the top of the sprocket cover)?
The cable is really tight you say. When you squeeze the clutch hand lever does the lever, cable, or release arm move at all?
Fuel going to the carburetor is a good thing, but it does not mean that fuel is going out of it at the correct air/ fuel ratio required to burn inside the combustion chamber.
Grounding a wire to the engine mount is strange.
There are only 4 wires of 2 colors to be concerned with.
Here's a diagram:
Do not worry about connecting the kill switch for now. Just work on getting the engine to run first. You can always stop the engine by applying the bicycle's brakes when the engine is idling (clutch engaged) or by when the engine is idling, turning the choke on.
Which carburetor do you have?
Does it have a black round air cleaner, a red round air cleaner, or a pink square air cleaner?