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.

If it's a 15 ampere circuit (the breaker protecting the circuit is 15 amp), then you can use 14/2 with ground between the boxes. If it's a 20 ampere circuit, you'll have to use 12/2 with ground.

Aside from that, it's a fairly simply install.

1. Run appropriately sized cable between the upper and lower box.
2. Connect the wires at the existing box (black to black, white to white, green/bare to green/bare).
3. Connect the wires in the new box to the receptacle (black to brass, white to silver, and green/bare to ground).

If you didn't already buy a receptacle for the new box, surge receptacles are available. Installing a surge receptacle behind the TV, would mean you don't have to try and fit a surge strip back there.

The side of the new box that's not enclosed, can be used to route data/AV cables down to cable boxes and such.

Update

The insulation on the wires appears to be old and worn, but it is clear that one is white and one is not. Not to mention, the white is attached to the silver colored screw, while the not white is attached to the brass colored screw.

Since there's no grounding conductor. You should replace the old receptacle with a GFCI receptacle. To do this:

1. Connect the white wire from the old receptacle (the one attached to the silver screw), to the silver LINE terminal on the new GFCI receptacle.
2. Connect the not white wire from the old receptacle (the one attached to the brass screw), to the brass LINE terminal on the new GFCI receptacle.
3. Connect the white wire leading to the new upper receptacle, to the silver LOAD terminal on the GFCI.
4. Connect the black wire leading to the new upper receptacle, to the brass LOAD terminal on the GFCI.
5. Place the "No Equipment Ground" sticker on the GFCI receptacle cover plate.
6. Place the "GFCI Protected", and "No Equipment Ground" stickers on the cover plate of the upper receptacle.