I didn't see the second part of your question. The direction of ||A x C|| or ||C x A|| doesn't matter because they have the same magnitude. That is why (1/2)||A x C|| = (1/2)||C x A|| is true.If you mean
Area of triangle = (1/2)||A x C|| = (1/2)||C x A||
as in, using the magnitude of the cross-product of two vectors to find the area of the triangle between them, then yes.