Sachs 505 motors will take Puch and comparable ignition and flywheels.
A pipe for a 50cc motor will work with a 50cc motor. You may have to measure,cut, weld, measure and trial fit to get the best results.
38mm rings will work on a 38mm piston if the ring width and end landing is right. You may have to measure and file to get the right ring gap and end-landing.
Handlebars are 7/8th of an inch. Electrical conduit, pipe, broomsticks that are 7/8ths will not work. Bicycle handlebars will work if they do not bump up to 1" If the center of the handlebar is bigger, you may have to measure, file, grind, to make it work.
bicycle brakes on a moped = not a performance upgrade = bad idea
motorcycle brakes on a moped = upgrade = good idea