DESTROYED STATE

If a unit would be destroyed after the "Defender Rolls Defense Dice" but stays alive as a part of an ability, order or Tactics card (e.g., Last Stand), does it suffer the Panic Test triggered as part of the Attack suffered?

Yes.

Can units that are Destroyed perform actions?

Community errata, at Pg. 7 of the manual replace :

“When the last Wound is lost from a unit, it is destroyed and removed from the battlefield.”

With :

“When the last Wound is lost from a unit, it is destroyed and removed from the battlefield. Destroyed units may not perform actions unless that action is specifically granted by an ability or effect.”