You could install a diverter on the roof of the shed dormer made of flashing like in this photo. It could keep water from hitting the roof over the stoop. This, however, may cause additional splashing onto the lower 1st floor siding. It already looks like paint pealing there. Looks to me like gutters is the solution.
One way for damage to siding: the flashing at the intersection of the little roof with the siding may have channeled water under the siding.
Alan
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