Roofing paper is not required by the building codes, although some do now require a plastic or rubber membrane on the lower overhang that extends up the roof to a point 18 inches inside the exterior wall. Although felt paper is not required on the rest of the roof, most shingle manufacturers do recommend it. It is not very expensive, it does give another line of protection against leaks and it also acts as a slip membrane between the shingle and the roof to avoid wear with the expansion and contraction of the shingles.
Although not absolutely necessary, I always recommend it.
For any roof with unequal water flow, the best valley flashing will be a "W" flashing. This is a sheet metal flashing that has a ridge pleated into the centre. The photo shows how the water jumps over that ridge and spills onto the shingles on the other side, rather than flowing across a flat flashing and sliding up under the other shingles. When water flow is equal from each roof, the water flow will meet equal resistance on either side and not flow up under the roof with less flow.