Mounting and centering a flat screen
It's drywall, and it looks like you have already torn into it and done some patchwork. I say tear the wall down! It sounds like a lot of work, but drywall is not that horrible to work with - for me it just ends up being time consuming since I always have to mud and sand twice.
With a TV that heavy and the down and out mount and all the "outward" pulling it's going to be doing I wouldn't mess around. The fact that there's a stud dead center tells you there's room for studs back there. My vote is for tearing out the drywall. I was on my way to doing this, but my walls are plaster, so it would have been a huge mess, and also - there is no room for studs back there in my house.