Drywall – Building a 1 layer thick brick wall over drywall

I'd agree with the masonry bit (as well, stucco is rough on drill bits anyway) of whatever size is recommended for the wall anchors you're using.

I'd been reluctant to post a response, as I had no idea what do do for the wall without flattening down that section, but I have a completely untested idea --

If the stucco isn't too extreme in its texture, and you're not going to be putting lots of load on the shelf, you might be able to cut a piece of foam to use as backing, and then tighten it to the wall to compress the foam so it's not too bouncy. You're likely going to want extra (or heavier) bolts for this; there won't be friction against the wall, so the bolts are going to be taking the whole load in sheer. Also, you won't have the same support against moment.

I was thinking some of the stiffer spray-foam might work, but if you wanted to make it removable without damage (and if you didn't, you'd just flatten the wall), you'd need to add some release agent, which might stain the wall, or go through some hoops to pull this off:

1. Make a frame the size of the bracket, open on the side against the wall, and an extra hole (see below).
2. Figure out where you want to mount the bracket.
3. Tape a plastic bag large enough to full the frame on the end of a can of spray foam.
4. Stuff the bag in the frame through the hole.
5. Hold the frame where you want to mount the bracket, and inject the spray foam.
6. Wait for it to set up.
7. Repeat steps 2 through 6 for each additional bracket location.

You might be able to do something similar with other products to mold to the wall, but all of the ones I can think of have slower set times which would make it really slow going.

Looking at your wall photos, can I assume that seeing hinges on both left and right, the doors (2) meet in the middle? first we have to make some assumptions based on the yet unknown. if the walls are always dry, seasoned and pose no moisture or condensation issues, there is a couple of ways you can go ahead and finish he walls with drywall. i would consider putting a 1X6 up to a 1X10 finish pine board in the corners. This should clear the hinges. You can then install 1X3 strapping on the concrete wall with PL400 adhesive and short ramset nails or concrete screws. You can then decide if you want to install any blue moisture proof rigid insulation between the strappings. Then install a vapor barrier such as 4mil plastic over the strapping and then install drywall with 1 or 1 1/4 inch screws. You then can finish your drywall and build a neat trim at the ends onto the finish pine boards. The other alternative is to build a regular frame wall out of 2X3's or 2X4's and mount to floor and upper joists. This will allow more insulation and still allow doors to open almost fully, depending on the width of the pine trim at the corners. The wider the trim in the corners, the more fully the doors will open without being restricted by the new wall. If moisture on the walls is possible, you should really consider using Dry-loc or some suitable waterproofing before you even think about closing the concrete in behind a wall. Mold and mildew with ruin your good looking wall and potentially cause foul odors and a possible health hazard.