I posted this under your "still confused" thread on 12/2. What happened? This thread looks like you never read it:
Next time you start a new thread, mention the moped make and model again. You know this, but those of us who are not busting knuckles on it tend to forget. Otherwise, this was a good explaination of the problem.
I think you are close to running, you are just getting lost in the big picture. Try to focus on one problem at a time and resolve it, or, if you can't, remember it before going on to the next.
Another thing to keep in mind is that 2 strokes are so simple, there is nothing to fix when they don't run. This makes repair very difficult. Anyone who owns a 2 stroke who tells you they have never had a "@#$% thing won't start problem", only to have it fix its self, is usually lying.
You are not alone, we feel your pain. : )
First, you need to figure out why releasing the decomp lever makes it easier to pedal. An earlier post sugested that it may be trying to run. I tend to agree with this except that with as much fuel as you have floating around you should be blowing mass quantities of smoke when it fires.
The decomp valve is a simple device, when you pull the lever, a small mushroom valve in the head opens to allow engine compression to escape. You should be able to hear this when you operate the valve, you may also see fuel escaping from the head in the area of the valve. When you release the decomp lever, a spring closes the valve and the noise should stop. You may have to let someone else pedal while you listen for this.
In operation, you operate the decomp lever to make the engine easier to turn over so that the centrifugal clutch can engage fully to turn the engine. As the engine begins to turn, the clutch is dragging which wastes some of your pedal power. When the engine turns fast enough to fully engage the clutch, this drag disappears and you are turning an engine with no compression which feels like a "mushy" load. When you release the decomp lever and get engine compression, you should feel the compression pulses but this is a 50cc engine and will not be hard to pedal, however, it might sound and feel "better". You may be mistaking this for "easier to pedal". Make sure the decomp valve is working and then don't worry about it, other than to get the engine turning.
Spark plug. This is the bane of all 2 cycles. Spark plugs can appear to work fine in open air, and never fire in the cylinder. The problem is that air is not as good an insulator as a compressed fuel/air mixture. Often, when the plug tries to fire in the cylinder, the additional resistance of the mixture and the plug being wetted will combine to cause the spark to leak across the surface of the insulator around the center electrode.
Buy another new plug or two. They do not need to be platinum, even if they are not the exact number, if the threaded portion is the same diameter and length, they are fine for testing. Just set the gap to your ped's spec. Each time you have tried to start your ped, take the plug out, if it is not bone dry, wash it with carb or brake clean and blow dry it with compressed air or shake it and set it aside to dry. Replace it with one of your clean, dry plug. Just for laughs, take any spark plug and gap it at about .030", laying on the head, this should produce a good fat spark. and tell you your spark is good.
You obviously know where the points are. Turn the engine slowly until the points just break contact. Using a pencil through the spark plug hole, make sure the piston is near the top of it's stroke (closest to the plug). If you are ambitious, 1 to 2 mm before top dead center is where the points should break. This does not have to be perfect to run, if it feel like you are near the top of the stroke, this is ok.
Trying to start the ped.
Turn off the gas and drain the carb if it is easy to do, it will save pedalling time. Now, using the decomp to get the engine turning, pedal like hell for way too long. Change the spark plug for a dry one and repeat. When the plug comes out dry, you have pedaled enough.
It is possible that while doing the above, the ped will spontaneaously start. You should be so lucky!
The purpose of the above exersize is to clean all the excess fuel out of the engine. Once a 2 cycle is flooded, you have two problems, the plug gets wet and leaks, and your mixture is not easy to lean out again. The above exersize solves this.
Now, check for spark using the "plug on the head" trick and install a clean, dry plug.
Turn on the gas, set the choke and pull the decomp. Pedal. As soon as the engine turns ok, drop the decomp, keep pedalling and slowly roll on throttle. Any more than 1/4 throttle is too much.
If the ped does not start, immediately turn off the gas, because we do not know if the carb is flooding yet.
Begin again at "Trying to start the ped.", but this time, do not use the choke and make sure that the last plug you use is not the same one.
One of the above methods should at least make some smoke and noise. Post the results.
It does sound like you could have some wiring problems. Do you have matching colors from the magneto into the ped wiring harness?
It would be unusual for the ignition to be wired wrong as this wire goes through the points to the ignition coil.
Someone mentioned burning out the headlamp because the tail lamp is not burning. This would make sense to me if the engine was running but I am amazed that you can do it by just pedalling. You say 12volt bulb. Any idea of the watts or amps? You should be using about a 25watt headlamp and 6 watt tail lamp.