Can I just add the coffee powder to the basket and let the the water vapour do the work or should I make use of a tamp same as with a professional Espresso machine?
The general idea is that tamping with moka pots is unnecessary/harmful/dangerous because of the excessive pressure this will cause (see Ivan's answer: https://coffee.stackexchange.com/a/489).
However, we usually compact the ground coffee a bit with a spoon by slightly tapping on the grounds while making sure that there is a flat surface. This tends to give a richer flavour if, for whatever reason, you do not fill the basket to the top. (E.g. if you want to prepare a smaller serving and you don't have a smaller pot.) This is not traditional tamping, but somewhat similar.
My hypothesis is that the reason for the improvement in flavor seems to be the longer extraction time: If the basket is only half full, I mostly tend to get underextracted, somewhat sour-ish coffee. Compacting the grounds a bit results in more resistance to the hot water and, thus, a longer contact time. (Not sure if that hypothesis is correct, but the result is easy to reproduce for me.)