The actual screen height is 82". The 36" x 80" dimension that is called out is nominal, meaning that it will fit a 36" x 80" door.
I would say no, this is meant for a single swing-in regular door, not wide enough for a sliding glass door area.
I found the assembly and engineering of the frame to easily install on my inswing door. It did not appear the framing would be suited for an out swing door. You may be able to install it but I'm not sure the appearance would be as nice. I would suggest contacting MMI and get their input.
The screen appears to be durable and strong. However pet proof is a subjective criteria depending on the temperament and size of your dog. Of my two Eng Springer Spaniels my male dog can go through even "Pet screen" materials.
I don't think so, it is made to mount to the door frame edge on both sides and this model is for an IN SWING door. MMI has great customer service, call them at 586-264-0950
I don't find the screen material to be as dark at the HD website photo. I believe the screening materials is enhanced for detail. It's typical screening material.