[bandito2]

Hope the guys haven't been scamming and taking advantage of you.

Seems obvious for a loose, poor(contaminated with corrosion possibly) or broken connection if it is quitting when you shake the bike. On the center stand /side stand issue may indicate that too by a connection failing/disconnecting because the bike is tilted. It could be an electrical grounding issue.

It sounds like a wiring issue. Have ALL of the engine starting, running connections cleaned and wires checked. Once it ever does get started, the idle may need adjusting so you won't need to keep giving throttle on start & idle.

There also might be a problem with the fuel delivery. Failing pump or poorly connected fuel pump wiring, plugged fuel filter or possibly kinked fuel lines. Fuses should be checked as well. I might have thought part of the problem may be trouble with the carb float, but since the problem persists after carburetor replacement, that wouldn't seem to be the cause.

Not sure how your scooter works, but on mine, the bike will not start or run if the side stand is deployed down, (a safety feature) but it will if just using the center stand. If yours is actually like mine in that respect, there might be a problem with the side stand switch.

HTH