How does the ruling work on Stealth Device and Prince Xizor?

Xizor's ability does not prevent him from losing the Stealth Device. Even if he passes the damage to another ship, it does not change the fact that he has been hit by an attack.

As noted being "hit" is all that is required to lose the Stealth Device. Even if Xizor passes off all of the damage he's still the ship that was hit and will suffer any consequences of that hit.

Draw Their Fire has the same interaction. Just because you can pass off the damage after being hit doesn't change the fact that you were hit.

Exactly so. You can be "hit by an attack" even if you suffer no damage - this is the basis of Lieutenant blount's ability, after all.