A ship with stealth device. When a ship takes a hit while equipped with this I know this upgrade gets dropped. But do you still take the damage as well

Yes.

Ok thank you

Side note. Damage from an asteroid would not remove stealth device.

Neither would auto-damage from Vader, Feedback Array etc.

So in order to loose a stealth device you have to be specifically targeted by the enemy?

It must be from an attack, so yes.

So in order to loose a stealth device you have to be specifically targeted by the enemy?

You have to be "hit"

Hit is defined in the rulebook as if, during an attack, there are uncancelled boom or kaboom results left in the dice pool after the compare results step then the defender is hit.

Any card that talks about being hit is referring to that definition. Anything that doesn't meet that definition is not a hit.