Ok, so I have seen mention of Mori being some evil half of Nori or something like that. I also heard Mori mentioned in quests...

Can someone clarify who she is and if you can do quests for her as well as Nori?

Mori is Nori's evil twin/other half. You can do quests for her between 8 PM and 8 AM EST.

If those are the hours, then it's changed very recently. The Wikia is wrong.

Keith told me the hours at the Anaheim 2010 meetup, because I had been telling people there was a twelve hour span and that you could affect this from doing quests, and neither of these things I was saying is true. The Day longer than Night for those quests and users can't actually affect the time. It was also held to be true by many users that the time varies by person/timezone and this is also not true it's always the same hours.

Alas I don't remember the actual hours I finished all levels of those quests years ago, and can't find the correct hours by Google, there's a lot of wrong information and wild speculation (complicated by the fact that people don't seem to be able to do the math for their time zone?) out there.