She actually has an order, but they don't exist on the NWN variant of Avlis yet. Once the Seven Cities go in, maybe they'd crop up.
Most likely not, since the last other member of her order was killed about 65 years prior to the current Avlis-NWN date.
But yeah, you don't need an Order... the fact that Monks are Lawful does not require them to find some sort of group to join, as is the "recommendation" in the PHB... Monks are Lawful because of the severe amount of personal discipline they need to follow the path they've chosen in life... one of the reasons why if you stray from that path before level 20 (take levels in another class) you can't return to the Monk path. Unfortunately, Bioware patched that feature out very early on in NWN's career, so you see a bunch of people just ignore that rule. Whether or not you follow it is a personal thing. I can't speak for all DMs, but I know a couple that would prefer to see Monks stick to that rule.
There's also the option of joining some other type of religious Order. An example would be AbominationFascination's monk, Quitstone Carver, (which sounds like some weird New English Deli Meat brandname) who is in a religious Order with clerics and such, but no other monks. Don't feel your monk has to be religious, either. While there is no way to be athiest in Avlis, your Monk's spirituality need not stem from a divine belief. A monk doesn't HAVE to follow any specific god... they could base their form around abstract concepts like Justice or Modesty. Conversely, you could base an entire style around stone... be strong like the stone, immovable, etc etc.
Now, you could take that as nature, and thus link it to O'Ma or something, just as you could take one of the abstract concepts like Justice, and apply it to Toran or Gorethar... that's up to you. But don't feel the need to HAVE to play a religious monk.
From the personal bent, Mina isn't very religious. her deity field reads Senath, (LN God of Strategy, son of Toran) whose colors she often wears, but it's a casual following... more of an ascription to his belief structure, more than an outright worshipping of him.
Hope that helps any other monks out there. If you need any ideas/help with Monk Orders, just ask me or better yet the team, in the event you want to RP a monk from some odd order, or want your monk to follow a certain god, but don't know if an established historical Order for it exists already.
Oh yeah, and don't feel the need to spout out random confucionist sayings, or impart wisdom on others... your wisdom could manifest simply in the fact that you're extremely perceptive, or just have an unprecedented amount of common sense/practicality. Don't feel like a monk has to be constricting, because it's actually a pretty flexible class, if you understand eastern religious mentality in the real world.