I have this wall that I'm wanting to make into a flat wall. I plan to use furring strips with rigid foam insulation on the bottom brick half. Then another wall of 2x4 studs in front of the existing ones, notching them for the PEX, etc. My question is, how do I go about setting this second wall on the ledge to make it flush? Do I align the bottom plate (which will be sitting on the existing ledge) outwards into the room to account for the foam board that will be on the brick face? Has anyone done something like this? I'm open to new ideas as well, just been building a bathroom to fit the existing layout.
If it was me I would use 2x2 steel stud in front of the brick ( assuming that gives enough room for required r value). Wood that thin doesn't really hold shape very well it tends to curve and banana. A disadvantage of 2x2 steel would be that it isn't very strong if you need to hang anything off of the wall. If you did need to hang something like a TV then you could frame in a section of three-quarter inch plywood.
In terms of running your pipes ensure that they are on the house side of the insulation. Do not bury water pipes in insulation if your region experiences freezing temperatures.
With this method you have one continuous plumb and flat wall from floor to ceiling. Then you are free to do whatever you want to do in behind it. I would add some ties to aid with lateral movement.