1)Yes you can use the TA01NSN with both eyes open. You can use any scope with both eyes open, although it will be hard to pick up the reticle since it doesn't glow in daytime like a bright TA31.
For Trijicon (and many members of this board) to say that a scope is "equipped with BAC" is actually a misnomer. BAC is a concept- A method of shooting with both eyes open, where the brain superimposes the reticle seen in one eye over the panorama seen by the other eye. You can use the BAC (Bindon Aiming Concept) with any scope, but most have trouble getting use to it. Trijicon makes scopes that have a reticle that illuminates with a fiber optic which really assist when using the BAC. It is not impossible to use BAC on a scope that is not equipped with a brightly lit reticle. The Trijicon fiber optic just makes it extremely easy to do.
2) The TA01NSN has yellow tritium that causes the center portion of its reticle to glow at night. The front back-up sight post on the outside top of the scope also has a green tritium element for night use. If you plan on hiding from people who are using NVD's, that green element may help them find you. If you are using NVD's, it may hinder your usage.