compass arrow direction

Errh? The arrow points to the north. When you go west, you will have north to the right, so of course the arrow will point to the right.

If whe are looking like this you are right
But, North and south are correct! When I ride to the North the arrow show the exact direction (to the top of the GPS) idem when I ride South (downside) but if I go to west the arrow go to the right instead of going left and vice versa for east when you look at a map the west is left (but I know you are right, a compass also show only North) .
It seams more easy for me to know in what direction I go then know where the North is, I was thinking I can change this somewhere into the settings

This is correct. When you are facing west the north is to your right hand side. When you face east the north is to your left hand side.

Specifically, which screen and compass arrow are we referring to? FWIW: The 820 does not have a compass sensor. It infers the compass direction from your GPS based direction of travel assuming the 820 is aligned with it. If you're not moving significantly, the displayed direction of north will vary randomly due to GPS position noise/drift.

Please take in mind I am speaking about the little arrow on the Map screen, I do not found something on the connect IQ site perhaps a (good(?) idea for the developers, this must be possible, no?
Now, it is not that important, if it exist I will install it or if I can change a setting I will do it ... else

I think I finally figured out where you go wrong:
You ask for a compass arrow, but what you actually want is not a compass arrow. You want an arrow showing your moving direction on a map where North is always forward.

Such an arrow would point forward when you go North, right when you go East, backward when you go South, and left when you go West.

The difference between this arrow and a a compass arrow:
The compass arrow will also point forward when you go North and backward when you go South. But it will point right when you go West and left when you go East.

in fact it is true what you say, I am not really going wrong but you are right: what I have in mind is not really a compass it is more a "direction indicator"

If you change the map to be direction of travel up then the arrow will always point in your direction of travel.

I know that I do not like that configuration I don't remember why, soon I go ride (when the weather becomes a little correct) I will try it and take attention to the arrow (it seams to me that there is nothing then, but I am not sure)

Yes. I keep north up rather than direction of travel up. I find this much less confusing or disorienting. Of course the little arrow in the center of the map shows my direction of travel.