When putting up furring strips or studs against a concrete wall in order to put up sheet rock, do I use a nail gun to shoot the nails into the 2x4's that go into the concrete or use concrete glue to hold the 2x4's against the wall for the drywall installation. Will I damage the concrete with nails. Especially if water can get through the walls of the concrete, because I had to waterproof the walls.

 

Construction adhesive and a couple of fasteners to hold the studs in place while it sets will do for fastening to the concrete wall. If you have so much of a moisture problem that the penetration of a fastener into the concrete is a worry, you might want to pursue other options. It may be better to build the wall out from the concrete wall, tied to the ceiling and floor. That way you don't have to damage the concrete surface.

 

Take a look at the basement section. Tons of info on basement wall building there.

 

If you're planning on just putting up furring strips to hang drywall they need to be fastened to the concrete walls with a fastner rated for concrete, simply gluing them with a couple of fastners to hold them in place, seems a bit iffy to me.

I'd agree that it'd be better to give up a couple of inches of room and just build yourself a subwall inside of the concrete sides, but I'd make real sure that I had my moisture problem solved with the waterproofing, or else provide for drainage of any accumulated water prior to sealing it up behind new sheetrock, the two don't mix well at all. You might consider treated lumber for your bottom plate if you feel moisture on the floor could be a potential problem down the road.