Do I have to report my findings of the head monk's murder to the detective to further the questline? He seems like a buffoon(even though I have my suspicions it's actually
Orin
) and I feel like my character being a pragmatic rogue would rather trust his own instincts to hunt the culprit, who I've already got a name for.

Also, I can travel to the lower city now. Will doing so halt this or Raphael's quest if I signed the contract with him?