Assuming the last pic is indicative of the worst damage it isn't a very difficult fix, but it won't be cheap. Remove the gutters and fascias, peel back the EPDM roofing (in my neck of the woods 13 years exceeds its service life anyhow), and cut back the overhang far enough to remove the rotted end grain, spot treat small areas of remaining rot with an epoxy stabilizer, and use a solution of oxalic acid to remove the black stains if you prefer to keep the natural finish. Skip the acid if you can live with paint. Before resurfacing the roof you really should consider adding some insulation, with the little I can see of that building in your pics it is going to be an energy hog. If it were mine, it would get at least 2 perpendicular layers of 2 inch rigid foam insulation with the seams staggered, capped with commercial base sheet (a 2 1/2" foam panel with OSB glued to one side), and roofed in rubber or PVC. Obviously this would include new fascias and proper termination bars for the roof membrane. This is not a job your average residential roofing company will be capable of, and in my area at least would require a commercial roofer. EDIT: This is what happens when I answer the phone in the middle of posting. Pushed to the end of the line.