What are furring strips and how would I install?
I am drywalling the upper brick wall portion of my working fireplace) so it can be painted and flat screen TV can be hung. Oh yeah it's going to look nice as soon as you help me out so I actually know what I'm doing is right... thanks in advance.

Furring strips are pieces of 1x2's attached to the wall. You will need to drill with a masonry bit and attach the furring strips with concrete screws and anchors I would also use liquid nails on the backside of the furring strips. Just be sure to run all your wires before adding the drywall.

I attached my 50" plasma to the rockwork on my fireplace without adding anything and it looks great!

Do not expect your furring strips to carry the weight of the fat screen, get anchors into the masonary wall. Also, the specs for the TV, some do not like the heat of a fireplace one bit. We see this app all of the time but may fail because the flat screen gets tooo hot almost by itself let along a fireplace.

Bob is correct on the anchors for the mount going directly into the masonary wall.
I do not use my fireplace in San Antonio... I burn candles in it for ambiance. My mantle is also very deep(15") and 70" wide.
They have fireplace hoods:
Fireplace Hoods (http://www.efireplacestore.com/fireplace-hoods.html)
Check the temperature above the fireplace after having a good fire going for about a few hours. Tape a thermometer where you want to mount the TV.
The temperature shouldn't be above 90 degrees. If it is consider placing the TV in another location or get the hood and a fan to blow the heat into the room. You can also have your ceiling fan going in the winter position.

Is liquid nails on a working fireplace a good idea?
Patty is right in asking how hot is the wall when the fire is going for a few hours.. do you burn a lot?are you in a cold climate?

When I found a glass fire surround on clearance it didn't fir my fireplace opening. I took 2" tubular steel and cut it to fit inside the rock opening. I attached it with construction adhesive liquid nails.....let it cure and attached glass door surround. I even primed and painted the steel. It's still good after 10 years and the paint is still there after many roaring fires. Just took the surround off to repaint it from the shiny brass finish it had and steel is still attached firmly. No more fires though since installing a 50" plasma above the fireplace.

I'm not sure what code is down there but up here in the northeast we can't have anything combustable touching brick... glad it worked out for you

I mounted the surround on the ouside of where the original black fireplace screens were. It's 4" away from the front of the fireplace.