What is the procedure for putting the stud into the crank?

The manual says:

CRANKSHAFT STUD: IMPORTANT!
When installing the propeller make sure the stud is screwed-in far enough to extend past the 7/16” shoulder of the prop hub. The crankcase stud must engage the thick part of the hub in order to provide the necessary strength. If the stud is not screwed-in far enough failure can occur possibly resulting in the loss if the airframe, serious injury or death.

What is the 7/16" shoulder of the prop hub? Are they referring to the hub on the motor or spinner side?

What do they mean by the stud must engage the thick part of the hub?

If you are talking about the 115, I thread it in till it bottoms out. Always have had enough bolt stickingout to tighten the prop. And remember the silicone to lock it in place. The stud holds the prop and hub on the engine. If it comes loose the hub could depart with the prop.

I have the 50cc.

What kind of silicone should I use on the stud? I think all I have is Permatex copper high temp. I might have some bathroom silicone too.

Here is what I have. I screwed the stud in all of the way (finger tight). I have 5/16" of thread showing after installing the spinner backplate, prop, and prop washer.

Is this what the manual is trying to tell me to have at least 7/16"?

Do I put silicone on the shaft?

I would want to be able to double nut the prop on so I would get a longer stud. I replaced mine (115) with a titanium stud also from these guys. http://www.yoyodyneti.com/ The HT Copper silicone is what I use, so far so good.

Do the gassers backfire or pop like the 4 strokes do?

Not much popping or backfiring, unless an ignition goes bad. The double nutting helps a bit to retain position as the wood of the prop compresses. I'd be willing to bet the 50cc came with two nuts.
As fas as where the shoulder engages, the stud needs to be screwed in far enough to get plenty of threads gripping inside the engine's crankshaft. By shoulder I guess he means on the crankshafts tapered end that the hub mounts on, and the stud screws into. Unless you remove the hub you can only guess where that is.