Gable vents should not be used IF you have a ridge vent. It short-circuits the soffit vent by supplying air to the ridge so lessens the soffits. Audel Complete Building Construction - Google Books
The water leaks over the doors/windows are from improper flashing.
1. No evidence that the tops (heads) were flashed with sticky flash or
2. If they were, flashing is also required
over the wood trim. Fig. 33 + 54
in the vinyl guild. This flashing top goes under
the Tyvek with diagonal cuts taped above. No evidence of that in pictures. Read page #8 of this again, look at the caulking under the top flange, then sticky flash going 1/4" on the flat edge of window head, then stuck onto the OSB---- then metal flashing over that, then Tyvek over that. Installing and Flashing Windows Correctly - Fine Homebuilding Article
As Inspector said, YOU tucked your raincoat into your pants. The vertical caulking bead is missing on the ends of the metal flashing to stop the wind-blown water from wetting the sheathing. You cannot rely on the J-mold vinyl to weatherproof your windows: Accept no siding that employs J Channels
3. The cantilevered deck should have a 2x4 vertical behind the handrail at the house, going down to the decking-with flashing under it. The joists should have a saw-cut dado under them to act as a drip edge so water will not wick back to the house. The solid blocking should have L-flashing under them with a drip lip to keep water from entering there.
The Tyvek shown, after demo, over the windows should not be under the window flange. When you nail the head trim after flashing, you will have a leak. Double flash, under and over the head trim.
Be safe, Gary