Can someone exterminate the Tyranids?

> 1. They just make everything out of jokes and madness, they see everything and nothing in their visions.

What prompts you to make this assumption? Not correct!

> Nevertheless, they massacre many a world

right ... just like Space Marines, Imperial Army and last but not least the Inquisition

> Not to mention Biel-Tan, they attack everything and everyone that comes into "their" territory.

Not correct. World ships have no dominion ... rather, the Eldar have dedicated themselves to the protection of exodite worlds.
What would people do if Eldar suddenly settled on one of their worlds? Champagne reception? Hardly likely.
What people don't know is that they are colonizing planets that belong to the Eldar => Eldar = pissed.

> 2 Well, I see it differently. How many Marines or Imperials would fight the chaos if they were damned anyway.

good point ... a few people noticed that and founded an association called the Inquisition.
How are the soldiers supposed to know that their souls are damned? Read in a book?
One of the most important factors in the cohesion of the empire is that the population is deliberately kept stupid.
And Space Marines are genetically modified fighting machines that are pumped full of combat drugs ... why, or how are they supposed to be afraid for their souls?

> Ojaa Dark Eldar are such friendly characters in the darkness of the galaxy.

Nobody said. Eldar and Dark Eldar have about as much in common as Chaos Space Marines and Loyale SM.

> Eldar in general are just messy

At D&D the correct term would be "chaotic - neutral".

> and if you don't follow your aspects you would go straight to hell (or into the soul stone) because otherwise you do something chaotic /> bad

I don't quite understand the sentence, but chaotic and bad are two very different pairs of shoes ...

> Everyone who does something nice supports Slanesh.

well, everyone has their own ... :-p