For the first problem, you need to find a normal vector that defines the plane. To do this find two vectors in the plane using those points and cross them:

Now this is the normal vector that defines the plane, we need to get the unit vector:

Unit Vector:

also

We must include both the negative and positive of this unit vector because it is perpendicular either way. I hope that's pretty clear, if not, I'll explain more just ask.

For the second problem, take the absolute value of the determinant divided by 2:

I believe these points to be co-linear since I calculated the determinant to be 0, but I'm going to check again. So for now, I believe the area of the triangle to be 0.