Event CE on Challenge quest

"Challenge Quest monsters are affected by Appearance Rate CE!"
Source: https://grandorder.gamepress.gg/halloween-2018-challenge-quest-walkthrough
So yeah, equipping both rate-up CE / event currency CE will affect your quest
However!
On the most difficult stages I don't recommend going with party full of event CEs - unless you have really strong servants - because this may literally lost you a quest
The easy ones are... just easy :D So don't hesitate here

I hope I helped, gl on farming&challenge quests!

Enemy appearance CE's +100 will increase the challenge quest difficulty also the drop significantly.
While the drop bonus event CE will work just fine.
I would not do that, but if you're strong enough to do that you're welcome.

I would only use the Event CE on the challenge quests which give a single type of event currency, so that leaves out the first 3 which gave a mix of 2 currencies, those are anyway not efficient nodes to farm.

Tbh, compared to Nero Fest, the challenge quests are "not challenging" at all if you hv properly lvl servants, so I like to have additional enemies to increase my drops and at the same time charge my servants NP for the final wave.