The 4 inch tube sticks into the aluminum peice about 3 and 1/2 inches, sticking out or the aluminum tube about 1/2 inch. Its holes must be in that end that stick out, as well as on the other end. The holes are the same on one end as the other such that you could put it in either way.
The nut is an odd one. I believe it is a 7mm metric. Keep in mind that when you specify a nut as being 6 or 7 or 8mm that that refers to the size of the hole, not the size of a wrench that fits it. If you cannot find a 7mm metric nut you may be able to cut new thread with a 1/4 inch fine thread die. You could also weld on a new threaded rod to replace the existing end. It is a rod about a foot long. Just remove the single bolt holding the muffler to the frame, then you can remove the muffler and work on it easily.
One comment about "performance" pipes. They tend to be a compromise. You may gain more top speed but at the loss of power on the low speed. I tried a Biturbo on my Puch Maxi. It gave a slight gain on the top end but completely destroyed the bottom end. It was absolutely gutless until I got up to about 22 MPH, and then its performance gain was only minimal.
An expansion chamber (performance exhaust) has to be designed with the port timing and port size of the cylinder taken into account as well as the RPM of desired power band. In otherwords there is no such thing as a properly designed one-size-fits-all pipe. The various models of Puch mopeds alone have at least three different cylinder port configuarations (maybe more that I don't know of) so any given pipe advertised for the Puch can't be made to work well with all of those variations.