I can't test this now on my own so I have to ask you.
When a trigger kills a unit via action, for example:
"Kill 1 Vulture at X"
does the vulture deathcount then automatly add 1 death for vulture?
And does remove effect the same?

thx.

No. I believe that Death Counts are counted only by game play based actions, not trigger actions. Meaning, if you killed the Terran Vulture using another unit, or some other means other then a direct trigger kill, then it would add +1 to the Death Count for that specific unit. You can add +X or subtract +X to the Death Counts via triggers, but you can't add Death Counts by killing a unit via a direct kill trigger.

are you 100% sure? It's just like you start with "I belive..." I want a 100% right question.

Yes.

Ok thanks
*pokes nude to close topic*

I tested this, and I can confirm it: Trigger actions like kill do not add to death counts.

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Topic was about to be locked, bronto already said that, and you may not notice din post 1: I can't test anything now.
Thanks for testing anyway

They don't, if you need them to, you're going to need like a kill area for units that you move them to to be manually killed.

If I again may elaborate on Falks answer...
When you kill x units, you never know how many you actually killed. Maybe there was no unit, but you think there was and (faultily) set the death count. Thus you move the unit instead of kill them. And make a trigger that checks if a unit is there and if yes kill it and increases the dc.