So I enhance my Rogue Three with Grey Squadron Gunner and Astromech Droid Upgrade .

My question is: Does Rogue Three now do 5 Unit / 5 Blast damage or 8 Unit / 5 Blast damage?

Rogue Three does gain +1U/+1B from Astromech Unit Upgrade and 2x +1U/+1B for the two enhancements being present. But is the effect of Grey Squadron Gunner based on the Blast damage Rogue Three starts off with (2) or the Blast damage it has when all "strike" effects are calculated (5)?

If it's the latter, you can almost one-shot the Executor with that combo ... that should make the DS think twice before they block your Rogue Three

If Grey Squadron Gunner's ability did not count Blast Damage and [blast Damage] icons unless they were printed on the card, it would have specified "for each printed Blast Damage and each printed [blast Damage]". Since it does not, it indeed counts all of the icons granted to the unit, meaning Rogue Three would indeed have 8 Unit Damage icons and 5 Blast Damage icons while enhanced with both Astromech Droid Upgrade and Grey Squadron Gunner.

EDIT: Relevant card text.

Rogue Three:

Blast, Blast
This unit gains Unit Damage, Blast Damage for each enhancement on it.

Astromech Droid Upgrade

Enhanced unit gains Unit Damage, Blast Damage.

Grey Squadron Gunner

Pilot (1) (Enhanced unit gains Unit Damage for each Blast Damage and each [blast Damage] it has.)

Agreed. Grey Squadron Gunner is a constant ability that continually rechecks the number of blast damage the enhanced unit has and adds that many unit damage. As long as we don't ever get a non-pilot enhancement that does the opposite it should be workable (otherwise we end up with a unit with infinite unit damage and infinite blast damage... though I guess that's only barely functionally different than Rogue Three with Astromech and Gunner.