Your roofing issues look to be the same as we faced after a new roof was installed. Did you manage to get it resolved? We found a new roofer to fix our roofing issues as did not trust the original roofer who installed the new roof. The new roofer installed new heavier lead flashing / back gutter along our chimney, and welded this (it previously was not welded and water droplets were rolling down the chimney wall). We also had some wet patches on the top side of the roof hip, which I believe is from water ingress somewhere along the hip, the original roofer did not cut the slate tightly against the hip and so the ridge tile overlap was very small. We are planning to replace the entire problem hip with a lead rolled hip, and hoping that resolve the issue.