Brackets on the nest box does sound like a good idea.
I'm a little sad about my coop now lol. Oh well. I'll just have to deal with things as they come.
It's not too late to get your money back...and then you can be glad again!
There are many great coop designs that take minimal skill to build and will cost you much less and provide more space than the one you've just purchased, so don't give up hope....there's a whole thread on BYC with coops galore that may give you some good ideas, as well as a whole coop page.
https://www.backyardchickens.com/t/596294/post-your-chicken-coop-pictures-here
https://www.backyardchickens.com/atype/2/Coops
And, to answer your original question, I'd not cover that window in the winter time...they'll need that air more than they will need the additional warmth...they have a down coat and feathers on top of that, so they don't need to be sealed up in the coop for warmth.