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?
You should not tamp the coffee in a Moka. These pots don't like excessive pressure, which tamping would produce due to increased density. This is also why the water should not cover the steam valve. In the worst case they can literally explode!
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.)