Martian,
Big job ahead by the looks of it. But could be worth the effort if you get your own AV room
The guttering inside a garage isn't something i've seen before.
You mention that the new front with PVC door is only going to be used as an emergency exit (you also said you may need to use it at other times) - doesn't really matter if you cover it with a screen for general use then. If its locked and unused except in emergencies, its not going to be a problem (as long as its easily thrown aside if the situation required it). If its retractable (manual or auto), then if you really need to use the door - its not a problem, as long as its not often.
As for the view from outside through the window - once its a habitable room with covered walls and floor coverings, etc - you'll want curtains or similiar on the window anyway, particularly if you're going to use a projector (help the darkness levels up and keep streetlight glare out).
At the end of the day - only you know how much you want or need to use that PVC door, and whats more important to you, the screen or the door access.
Unfortunately with doors at both ends, somethings got to give (unless you can find a way to get the screen right out of the way of the door).
If it can be recessed into ceiling plasterboard and that helps - all the better.
Its does looks a lot of work (gas box, drains, pipes, and a utility room built in) but im sure you'll get there. And then we'll hear just how much you're enjoying it
Good luck, Mark.