So this is what I understand of the Paralyze condition.
When a model is paralyzed it forfeits its activation, then the condition is removed. If you gain it during your activation, it ends there. If you gain it out of activation, it ends at the end of the models next activation.
1: Sue activate, Harm for card, (0) ability Man in Black, 1AP attacks model and loses terrifying duel. Sue is paralyzed, Man in Black stays active until end of turn, activation ends and condition is removed.
2: Nures meds Sue, who has not yet activated. Sue is activated, forfeits his turn, activation ends and condition is removed.
3: Nurse meds activated Sue. Turn ends, all activated abilities end. Next turn Sue activates, forfeits turn, activation ends and condition is removed.
Harm is an activated ability and could not be used, in the same manner as (0) abilities.
Hard to Kill would still work, as it is a non-activated (passive) ability.
Jack could still push and Obey him, if he is Tormented.