I'm curious about that too but I guess them keeping a low profile is the most likely answer to that. It might be more than that though.
Regarding Mamizou, the Hakurei shrine exist in both sides and you can enter from there. She probably knew about it and entered from there. As for Nue, I dunno. I remember I've read somewhere about Akyuu mentioning that some Youkai sometimes formed a group and went outside the border to hunt for humans but I believe they need permission from Reimu or Yukari. Maybe that's how Nue got out?
To be honest, I'm more curious about what Byakuren were doing during her time in Hokkai. It is already revealed in SoPM that her seal only prevents her from going out, she's not bounded or anything. I like to think that aside from reading sutras, she spend her time there traveling around Hokkai, bumped into some material that was later made into her scroll, maybe fight some beings there, or found some other interesting things if Devil's Recitation is any indication.
I got this idea after reading a doujin. While Byakuren is in Hokkai, Shinki got interested in gaming and created some monsters from MH and the demons from SMT(including Hitoshura) that Byakuren ended up fighting(read: befriending). Pretty much doing a training in hell.
I had hoped that maybe she'll talk about Hokkai a little in HM but unfortunately she didn't. That would've been interesting since it could shed some light about that place. Of course, she might actually just spent her whole time reading sutras. But man, 1000 years, she's got some patience.
Also, regarding her magic, she basically have two. Buddhist magic that was taught to her by Myouren, which she probably perfected after his death, and her so called 'evil' Dark magic, which is pretty vague other than it is said to come from youkai and is the key to her youth. I'm curious about what made hers particularly 'evil', I thought we'll see some of it in HM but I think they didn't mention anything about it. I think we don't have enough info about it so I won't go there.
What I'm wondering is, which one is her 'buffing' magic? If we go by HM, she should be using her Buddhist one, what with the names and such, implying it's her buffing magic. However, in the wiki or her profile, it's said that the magic that is demonic in nature is the buffing magic, or there might be some mistranslation here. For a human to turn into a magician youkai, they must keep training their magic, usually the one they specialize, until they become a youkai. That's why I figured that her buffing magic is her demonic one, but I'm not so sure now.
Is Byakuren using a combination of her Buddhist and Youkai magic? Or she's still hiding something more?
While I'm at it, how good do you think she is compared to Marisa, Alice, and Patchouli in general about magic?
I like to think that she's better than even Patchouli, she won't be called a Great Magician for nothing, right?
What do you guys think?