Can you perform interrupt abilities while stunned, such as quick draw?

no if it means you will attack or exit your space with your interrupt. quick draw implies an attack , and stun card is very clear. You cannot attack or exit your space "voluntarily"

On a slight tangent, if you are stunned, and it is that model's activation, could it remove the stun with the first action and then move or attack on the second action?

Yes. Exactly like that.

When using the command card "Lure of the Dark Side" on a stunned (hostile) figure. Will this figure be able to attack? Or in other words, is this a voluntarily attack?

I'm at work and can't check the card but does stun read the same way as bleed? I ask because bleed specifically states that it is during your activation that you take strain if you don't burn your first action... since it qualifies that it is during your activation you could interrupt with an action while bleeding without taking the strain.