Let's start with the plywood. The weight of the TV (and don't forget the weight of the mounting bracket) is not that large. Books on shelves routinely weigh much more than that. And most of the pressure is downward. You probably could get away with 1/2 inch board, but I would probably go to with 3/4 to reduce bowing.
Your proposed frame for the plywood seems very wide without middle support. I would add horizontal members across the top and bottom that extend over the vertical window frame members, and an upright in the middle. Your illustrated uprights, as well as my suggested middle brace, could fit between the upper and lower horizontal supports.
I would attach the plywood to the frame with numerous wood screws, probably #10 or 12, about 2" long. I would space them no more than 8" apart. I would attach the plywood/frame structure to the window framing with lag bolts, through both the plywood and your new framing. I would use at least four lag bolts on each side, probably 5/16 or 3/8, long enough to reach 2" into the studs behind the window fascia boards. All screw holes should be predrilled.
I think the best approach to mounting the bracket would be to use bolts and nuts with large fender washers through holes drilled in the plywood. Probably 1/4" bolts.
You can do this. But, as Paulster2 suggests, you need to consider whether you should.