Why is the electric flux defined as (electric field) x (area), Φ = EA? How do you come up with that equation? Is it because the electric flux is proportional to the charge and surface area?
That's close, although it's not quite right to say that it's proportional to the charge; you can get the same amount of flux through a given surface with a small charge nearby or a larger charge farther away. That's why the field strength E appears in the formula.