Basically, I've drawn the diagram and considered the fact that the geometric definition of the cross product is: U x V = |u||v|sin(theta).

Given that the angle between them is pi/6, then sin(theta) is equal to 1/2. So, I see where they get the 1/2 in the answer. However, these are my questions:

1. I'm unsure how to relate the 1/2 to the vector (e3) perpendicular to the plane spanned by e1 and e2. How do they relate?

2. Does normal basis mean each of the vectors in the basis is a unit vector and that therefore there magnitude's are all 1? This would simplify the problem but i'm not sure if it's correct.

Correct.
Any ideas would be appreciated and I will definitely click the little thank you button for you