How did they get away with a third layer of new roofing on there? Maybe it's ok in your local area. I would have a roofer look at the roof/wall intersection above. With stucco, I'm betting they didn't re-flash the junction since the 1st layer of composition.
Repair the wood, paint it, and flash it. Why doesn't the gutter return there? That looks like some deep rot, I suggest to call a professional. Be safe, G