If G4RG0R (initiative 0) has a buzz droid remote at range 0, does he take the damage before or after he engages? If before, and the damage destroys him, does he still get to shoot?

Buzz droids have initiative 0 and say: Engagement Phase: At your initiative, each enemy ship at range 0 suffers 1 damage.

39 minutes ago, player2072913 said:

If G4RG0R (initiative 0) has a buzz droid remote at range 0, does he take the damage before or after he engages?

That depends on who is First Player. First player would activate their ships & remotes first, and resolve all of their effects. Then, second player would activate their ships and resolve their abilities. In this case, if Scum was first player, G4R-GOR would shoot, then the Buzz Droids would deal it critical damage. If the Separatist player were first, then the droids would first deal a crit, followed by G4R-GOR taking its shot.

39 minutes ago, player2072913 said:

If before, and the damage destroys him, does he still get to shoot?

Due to the Simultaneous Fire rule, all ships within that initiative bracket (in this case, "Zero") will get the opportunity to engage. Even if the damage would be enough to destroy G4R-GOR, the Scum ship will get to retaliate (albeit, with the additional effect of the just-assigned critical damage, which could prove problematic).

Reference images!

2 hours ago, emeraldbeacon said:

D ue to the Simultaneous Fire rule, all ships within that initiative bracket (in this case, "Zero") will get the opportunity to engage. Even if the damage would be enough to destroy G4R-GOR, the Scum ship will get to retaliate (albeit, with the additional effect of the just-assigned critical damage, which could prove problematic).

Just to add one more note, the Simultaneous Fire rule also applies to Remotes, so if G4R-GOR were to destroy buzz droids sitting at range 0 of another ship, they would still deal that ship a crit before being removed.