When skill drain is active on the field can i tribute card car D to draw 2?

Yes. Activating Card Car D's effect is a cost, and it's effect activates in the Graveyard. Since Skill Drain does not prevent Activation of an effect and only negates effects of Monsters face-up on the field, Card Car D's effect will still activate.

Nice xD thx
Now i can play it in my skill drain deck

How about Effect Veiler and Fiendish Chain?

Eg. For Exiled Force, its effect will be negated in the graveyard if it was 1st negated by veiler when it is on the field.

So I am not sure whether effect velier will do the same to card car d.

And for Fiendish Chain, I am not sure how it will affect card car d.

Effect veiler negates the whole thing.

Skill Drain/Fiendish chain only negates a face up monster.

Ｑ：このカードで選択されているモンスターは、自身をコストとしてリリースして発動するモンスター効果も無効化されますか？
Ａ：いいえ、対象をとる関係がなくなるので、無効化されません。(09/11/14)