Thank you everyone for your input and photos. After giving it a lot of thought, I have decided to go with the brick. Mostly because I think it will be a good idea to tie the inside of the house with the outside. I also stacked some of the bricks being used for the outside up along the fireplace wall and I think it looks really good. Thanks again for the input.

Don't quite understand the base.But can be 2 different problems causing this .. 1-the base can be moving not built right .. 2-The wall in the house that is showing being pulled away was not anchord to the frame wall when it was being built.Meaning wall ties were not installed or not enough...The base you see from the basement usually is for the hearth and should show a cantilever.. The upstairs wall is supported from the concrete foundation... But like I said can't quite understand what you were saying

No problem covering the brick if it is sound but there are codes governing how close combustible materials can be to it at different distances from the firebox. Where it is close to the firebox opening (see local code) it must be as thin as possible (like 3/4" tile, granite etc) in order to not change the firebox design much and non combustible. The finish wall surface can be farther out where it is beyond the required noncombustible surround (see code).

Just so you know, the studs you used are too close to the fireplace opening to be safe and it does not meet code. You should float it all out with non-combustible material such as brick.