Biggs' ability does not affect Dengar's retaliation shot.

That is to say, when triggering his ability, Dengar may shoot at the ship that attacked him, even if Biggs is also in arc and at Range 1 of the attacker.

Correct or not?

Correct. Because Dengar's revenge shot specifically says it targets the ship who attacked him, it cannot target Biggs (unless Biggs shot him of course), so it is free to proceed as normal.

This is generally true - if you get given a shot which cannot target biggs and for which you don't have a choice of weapon, you can always use it.

The other key ones in this case being IG88B's pilo ability - if you miss with a primary shot (presumably vs Biggs) you then get to make a Cannon shot, but if he's at range 1 and you have an HLC equipped, you can still do it to someone at range 2 or 3. Same with the Ghost with the Phantom docked - if you attack Biggs with your primary at range 2, you can then potentially make a free Autoblaster Turret attack on someone at range 1 regardless of Biggs' ability at the end of the round.

E: in summary, Biggs basically says 'if you can attack me, you must do so, attack someone outside my range, or not attack at all, even if you have to choose a weapon you might not want to choose to do so'. If you can't attack him at all with the attack in question because its targetting is limited and/or it doesn't offer you a weapon choice and he's out of range of the relevant weapon, his ability never triggers.

I'd say you are correct.

Because in the case of Dengar's retaliation shot, Biggs wouldn't be a valid target... Although there could be an argument that if Dengar hasn't used that yet, he would have to use it against Biggs. I'm not sure it's a strong argument, but I thought I'd mention it.

Right, Dengar says, "you may perform an attack against that ship." You're restricted to attacking the ship that attacked you, so you cannot legally target Biggs. If Dengar said, "You may perform an attack," then Biggs would take effect.

E: in summary, Biggs basically says 'if you can attack me, you must do so or not attack at all, even if you have to choose a weapon you might not want to choose to do so'. If you can't attack him at all with the attack in question because its targetting is limited and/or it doesn't offer you a weapon choice and he's out of range of the relevant weapon, his ability never triggers.

E: in summary, Biggs basically says 'if you can attack me, you must do so or not attack at all, even if you have to choose a weapon you might not want to choose to do so'. If you can't attack him at all with the attack in question because its targetting is limited and/or it doesn't offer you a weapon choice and he's out of range of the relevant weapon, his ability never triggers.

Quibble: Biggs doesn't prevent you from attacking ships that are outside of his ability's range. When I'm trying to explain Biggs to new players, I tend to use the metaphor of him flying over to intercept rather than forcing you to attack him. That model has its own weird corner cases (like weapon selection), but I find people sometimes forgets that pilots who aren't close to Biggs are still fair game.

Myself included, I've made that mistake more than once. I've made an edit to my post.

i believe the new faq explicitly points it out that he doesnt have to target biggs for that attack.

It does, the FAQ says...

When Dengar is attacked by a ship that is at Range 1 of Biggs Darklighter, if Dengar chooses to use his ability, he attacks the ship that just attacked him rather than Biggs Darklighter.