Electrical for built-ins and fireplace insert
1) you could use wiremold. They make 90º inside corners. I don't like it but if you have use it then it works. Better off to chop a new box in the wall exactly where you want it.

2) There are several ways to put power wiring behind the planks. EMT, ENT, wiremold...there are others less often used. You will need an extension box on the left power box to run out of.

3) The bricks around should just be a facade but why make it hard on yourself? Just bring the TV mount area out far enough to have the media box behind it.

4) Putting power in the back of the firebox will probably be a major pain. I believe that is firebrick surrounded by other brick. You may need to get a bricklayer in on this. Or at least you should study the construction of fireplaces.

I see other problems here, though. The National Electrical Code requires that no point along the floor line be more than 6' from a receptacle. If you cover the receptacles on left and right will there be other receptacles on the wall line close enough to satisfy that requirement? If not you will have to add them. Also, you can't cover junction boxes they have to be accessible inside the cabinets.