(Ally) Faramir’s Card reads; “Action: Exhaust Faramir to choose a player. Each character controlled by that player gets +1 WP until the end of the phase.”

I exhaust Faramir right before Quest Phase. Does this mean since he is exhausted during Quest Phase , he cannot commit to a quest, thus as a result his WP doesn’t count in Quest Phase?

Correct.

Technically I assume you are exhausting Faramir *in* the quest phase, not before it, so that Faramir will increase their willpower during questing. There are two action windows in which you would typically exhaust Faramir, before staging or after staging. Unless there's some reason to exhaust before staging (such as a treachery that discards 0-wp characters), it's usually better to wait until *after* you see what has come out of the encounter deck before exhausting Faramir. That way if you don't need or want the willpower boost you can use him for combat.

And so he isn't damaged by Necromancer's Reach, etc.