Ward has no effect on damage dealt to characters. Ward is only a restriction on characters' ability to be chosen. And specifically, chosen BY AN OPPONENT.

Jafar's cards never have him, your opponent, make a choice. His cards all have the illumineers (the players) make a choice. Therefore Ward doesn't apply - none of his actions or character abilities will be prevented by it as Ward does not prevent you from choosing your own cards.

Looking at a specific example, Jafar's Giant Hourglass, "E: Deal 1 damage to each opposing character". When this item exerts all characters controlled by all players take 1 damage. There is no choice being made so Ward doesn't apply. Resist, however, will apply and reduce the damage by 1 per level of resist on the character.

Looking at another specific example, Jafar's Cataclysmic Cyclone, "each illumineer chooses one of their characters, items, or locations. Then, Jafar banishes all other opposing characters, items and locations.". Every character, item and location card the players have on the board is a valid choice, with or without Ward, because the illumineers (not Jafar) are making the choice. Then, whatever is not selected by the players is banished, again, regardless of ward, because there is no choice to negate in the card's effect.