The text of this card says:

Action: when this unit attacks, it inflicts 4 indirect damage points to all enemies (every player asings its own indirect damage)

Does this means that when the descendent of indraugnir attacks, it deals 4 indirect damage AND its 4 damage points? or just the indirect? or can you choose if you want indirect or just the normal attack points?

Thank you for your time

Its both, first the 4 indirect, then the 4 combat damage

So ID is assignes first at the moment of attack - right?

Does this mean that if DoI attacks a zone with 3HP left and it is not blocked the defending player can assign the ID to the attacked zone and burn it thus rendering the normal damage useless?

And just to be sure: if DoI is taken out by defending units with Counterattack indirect dmg is stil applied?

DoI's ID is assigned as soon as it's declared as attacker. That's before defenders are declared, so counterstrike don't apply yet.

And yes, you can assign the ID damage wherever you want, but you can't assign more ID than what is needed to burn a zone or destroy a unit.