The correct color is a bluish/gray that is available from most part suppliers (I get mine from NPD). The uprights, the vertical parts that the grill bars attach to, should be semi-gloss black. The attaching tabs on each end of the top should also be semi-gloss black.
Yes, all parts were painted separately and then the grill was assembled. I have seen original grills with the rivets on top either painted black or with the bluish/gray paint swiped over the rivet head. When the bluish/gray paint is used to cover the rivet heads, the color is usually noticably different and there are brush marks present.