Sword spec never procs an off-hand attack.

Does Sword Specialization proc on offhand tbc?

To answer all of the questions, yes, if you have a Mace/Fist in your main-hand with a Sword in your off-hand, and points in Sword Specialization, then the sword has a chance to proc the Sword Spec.

Can sword spec proc off windfury?

It is a common misconception that Sword Specialization can only proc off of normal (white) swings. This is not the case and is likely confusion over Windfury Totem. Windfury only procs off of normal (white) swings. Sword Specialization procs from all damaging attacks, including special attacks.