answers (i think)

4) so if i know the area vector, then i can dot it with the vector field to find the flux. once they're crossed, it will be obvious what conditions will allow flux to be positive.

5) the same is true for this one, right? if i know the area vector, i can just dot it?

6) i have no idea since it's not a flat surface. the only thing we have learned is the divergence theorem, but this won't get me anywhere being that the derivatives of a, b, and c must be zero since they are constant.

any help would be greatly appreciated.