So I emailed the lecturer about enrolling in Complex Analysis without having done two 2nd year maths subjects and I get this back:
"I sought advice from the relevant committee in the Department, and received
the response:
Complex Analysis is meant to be a capstone which pulls previous ideas together. Nevertheless, it is an advanced subject and the student should be picking up some more skills first.
In view of this, it is therefore not possible to waive the prerequisite."
C'mon...I mean how much could doing something like Vector Calculus prepare me for C.A.?... 
For the last one, there is a proof of the Cauchy-Riemann equations that uses Green's theorem. Also, contour integrals in complex analysis are pretty similar to line integrals in Vector Calculus. I mean, contour integrals are very similar to 2D line integrals.
My knowledge of Complex Analysis is quite limited so I can't give anymore information I'm afraid.
Only a pure math major thinks what they do is fun 
Ill have to see...might push it to 3rd year. My dream study plan is kinda ruined now... 
Isn't that the point? It'd be pretty depressing if they didn't think pure maths was fun. It looks boring enough to me.