If I played Ageless Crone and my opponent played Assassination would the cost not only be one extra fate but one extra honor as well?

No, Ageless Crone is specifically referring to the Fate Cost to play an Event. Not the Ability Cost on the Triggered Ability. Notice the term "play" in her text. The Ability Cost, after the bold colon and before the dash, is the cost to trigger the ability.

"During a conflict in which this character is participating, increase the cost for each player to play each event by 1."

Already asked here , if you want further reference.

Dev ruling sighted.

http://www.cardgamedb.com/forums/index.php?/topic/37988-ruling-kakita-yoshi-ageless-crone-fate-cost/