I'm in New England. I have 4 hens 1 rooster in a 10x10 for years. There is a shelf from one end to another with dividers in the middle to section off 5 nests. That gives them under the nesting boxes, and the rest of the coop to exercise. Oh yes they have a perch that runs from one end to the other of the coop (same direction as boxes but not over top). I have two doors (they slide up and down by a cable through the wall hooked outside) one in the back one on the side. Winter, only the back door gets opened (less windy in back). I open when I get up and leave for work. I close before I go to bed, they are already in bed by then. If it becomes freezing they stay in, no problem. I keep 24/7 grain/cracked corn in a hanging feeder, fresh water (heated) in a corner so not to dump over and a dish of black sunflower seeds in the other corner. Evrynight after our dinner, they get leftovers. Sometime there are days they stay in all day. In the summer all doors open 24/7, all windows stay open. ( I have person door too so I can clean) They have a run that surrounds 3 sides of the coop, fort knox actually. So the come in and out as they please. Easy. They are on my time not me on theirs.
I have new hens and they lay in the same nest. They are fast egg layers and when I first got them (3 months ago) the bottom eggs were crushed before I realized there were so many. Not sure why they never use the other nesting boxes, my other hens always used their own separate boxes.

To answer your questions:

*to close coop door in winter -
vinyl will not be enough closure for windy nights
plus water will freeze inside if coop isn't kept warm enough
in your climate you may need a heated water base in winter
can be homemade with a light bulb fixture attached inside a upturned bucket

*can reduce cold wind by attaching plastic sheeting on 3 sides of the run. We have protection of forest and our coop isn't out in the open. Others use the plastic sheeting or fiberglass panels on the side of prevailing winter winds. Imagine it is like a greenhouse with the protected run.

we reuse old tarps on our run to cover it. Someday will switch to fiberglass panels when we redo the various repurposed welded wire fencing we first used. Needs to be strong because of the forest debris that falls

*we close manually with a track for the door to slide up or down by a cord along the wall through a hole in the front with a washer on end of string that when pulled down & door is open loops over a cup hook. Plus a bit of ribbon on the washer helps us see from the house whether open or closed. Our kids were K & 3 grade when they started raising chickens, so it was helpful to supervise their work.

concern because of raccoons & possums who manage to show up in fall hungry for chickens

Numerous times kids in our 4-H club have sad stories about losing chickens one by one or the whole coop in a night from predators. Closing up the coop with a solid door prevents that.

*about nesting in corner on floor - is the nest box large enough for them to turn around 14 inches or more square

chickens will nest where they feel safe and it's darker lighting

may also be nesting there because one started laying there

try putting dummy eggs in the nest you want them to use
(even golf balls or rocks work as dummy eggs, so you don't have to buy them)

hope that helps

Thank you for the information. I bought an EasyGrow 8x8 greenhouse on Craigslist. I plan to move the coop inside during the snowy part of winter. If I put the fan on either a thermostat or a solar timer doyou think thre would be a humidity problem. I can put a fence around the structure to keep the raccoons and such. Would a shock fence work better?