I wonder where all these wires SHOULD go, and who wired my car like this and why... I don't understand it, and I don't even know what all these parts on my car are: http://www.cardomain.com/memberpage/570883/6

That appears to be an external washer fluid pump that someone tapped into the stock wires to activate. That round gizmo with the black plastic cover is your wiper motor, the pump inside it probably croaked.