All you need is a 2-8 x 6-0 door, should get you in. It will not be a stock door, but shouldn't be overly hard to get if you have a door shop near you.
The window in the picture has what is known as integrated trim, they are typically used in conjunction with vinyl siding. They are not designed to have an additional trim board.
Not sure what the lead time is in your area, but I am a builder in Central NH and we a literally booked until next June at this point. Granted we are a small mostly custom build company, but if you don't already have your builder lined up you probably wont get one before your deadline.
I have put on a few metal roofs (builder by trade) in NH. Almost every manufacturer will tell you that an underlayment is required. We typically use a synthetic product. You can use the other panels, as long as the screw holes fall in the right location. I would second (or third) the...
I can easily see the contractors point here. He is going to invest the time to work out a full materials list as well as asking his sub contractors to do the same. His time is worth something. The other way to look at something like this is simple, if he did all the work of lining everything...
If you can, verify that you have a complete circuit (and the correct voltage) at the thermostat wiring. Also on some models (not super familiar with the one you have) the vacuum switch cannot be closed (IE jumped) before the blower motor starts. I doubt it is an igniter problem, based on what...