Is white used as base paint before other colors? So is the paint on coloured parts thicker than in white parts?
Not always. This video (screenshot below) shows an ex-US-Airways A319 being redecorated in the American fashion. While the blue and red paint for the tail detailing is indeed applied on top of a white undercoat, the blue and red paint for the detailing on the mid-to-forward fuselage is applied directly on top of the yellow primer coat, with no white undercoat; the coat of white paint on these parts of the fuselage goes on top of the other colors.
That said, some browsing through airliner-painting videos gives the impression that, although a white undercoat isn't universal, it does seem to be surprisingly common, even for liveries that otherwise have little or no white.