Need Advice - More and More "leaks" In Every Room

We live in Northwest Arkansas and have just had a new H-Loc Standing seam roof installed about 4 months ago. Our roof is almost flat - 2:12 pitch. The ceilings are cathedral with exposed beams in almost all areas. We have the usual pipe venting, a fireplace chimney, and six round skylights (that do not open) on the roof. The contractor pulled off all the old brittle roof shingles, and claims to have put synthetic underlayment over the existing plywood before installing the metal roofing. (Side note: At the same time we had the whole house vinyl sided ((different contractor)), removing all the old composite shingles ((from the late '70s I don't believe is manufactured anymore)) and replaced with light beige vinyl.) I have looked through countless blogs to get advice on what to do about all the condensation (?) and/or leaking (?) onto the ceilings in 99% of every ceiling on the upper floor of the house. Here are the issues we are having: During the past few month at times when it was colder than usual, we first noticed that our front storm door had an unusual amount of condensation - then solid thick ice, that we never saw before getting the roof replaced. We shrugged it off thinking it was just because of the bitterly cold temperatures outside. Outside the front door under the carport, the siding - starting at the crease where the ceiling portion meets the siding wall - started to sweat rivers all down the outside wall of the siding (UNDER the carport). Brown rivulets of water all down the side of that wall. Next we noticed that when we opened the blinds, all the windows in the upper floor of the house had lots of condensation every morning - even though the temperatures outside has not been as cold. Next we saw the first two brown spots in the middle of the upstairs bathroom (where there is not a cathedral ceiling). We called the contractor, and he sent the worker over. The worker said he "forgot" to caulk around the vent (boot) directly over that spot in the ceiling. He came over, applied caulk, and left. Next day or two goes by and there are more spots in that bathroom. These spots are in the crease where the ceiling and wall meet - and basically on the interior side of the "sweating siding" wall mentioned previously on the outside of the house. Over the last few weeks we have seen more and more spots every day. Again on the bathroom ceiling, and now the entire perimeter of the living room, some in the kitchen (no cathedral) and hallway. This is happening where there are skylights or the chimney in the vicinity of the water leaks/brown spots, and also there are leaks/brown spots where there is nothing around it but roof. The contractor is trying to tell us that it is our fault because there is not enough venting and this is causing too much condensation. It's raining right now and I see a wet spot growing in the corner of the living room - under a sky light. What is your advice to rectify this disaster of a roof issue? Help?