Heavy Blaster Emplacement tells my opponent to damage one of his units. What if the only unit he has in play is Executor, which if not already damaged, cannot be targeted by enemy card effects? Could it be damaged by the Heavy Blaster Emplacement?

Short Answer: yes.

Long Answer: The Heavy Blaster Emplacement reads " Action: Focus this enhancement to have your opponent deal 1 damage to a unit he controls."

The enhancement is not targeting a unit (in this case Executor). You are focusing the enhancement and forcing your opponent to choose a unit. In the same way cards like X-Wing Escort don't target a unit but force an opponent to take an action and can still effect the Executor. Unless the effect specifically mentions "target"-ing a unit it can still effect those immune from being targeted.

The key word here is TARGETED. If the card effect specifically tells you to TARGET, then Executor is unaffected by that card effect. Not TARGET keyword? Then Executor is vulnerable.

Agree with everything said, just as a further parenthetical, the undamaged Executor "cannot be targeted by enemy card effects", and the above explanations address targeting... I just what to highlight that targeting is permissible if not dealing with "enemy card effects."

For example, resolution of Tactics Icons is an enemy effect, but it is a framework effect, not a card effect (for Tactics, the word "target" only appears in the rulebook). The placing a shield token on the Executor via Sabotage in The Snow or removing a focus token with Motti would be a targeted card effects, but not enemy ones.

Also worth noting that Targeted Strike can still hit the Executor as well.

Yes. Making Han a little strange vs the Executor because the first time around he can't trigger his reaction to ping it, but when combat begins he can targeted strike the Executor. Next round Han can then ping the Executor when declared as an attacker because it's already damaged.

This is of course assuming he doesn't run face first into the Executor and die.

Chewie's also awkward against the Executor because you can't react for double damage against it until it's damaged, but you usually are striking second when Chewie's blocked.