Drywall – How to block off a doorway with studwork on a brick wall

You cannot remove this fake brick without damaging the drywall under. You will have to replace the drywall, best solution, or do one hell of a good skim mud coat over the damaged drywall. You can use a Rockwell Sonic Crafter or similar tool to cut the drywall cleanly at the edge of the cabinets. replace the drywall, mud it in, and paint. There is no easy way in this case.

If the new wall joins in the middle of the existing wall (eg making a T shape), you can use either wall starters (eg such as these ) fixed to the existing wall to accept both the inner and outer leaf of the wall or you can use frame cramps (eg such as these ) fixed individually for both leaves of the wall.

If the new wall continues along the same line as the old wall (ie it joins it at what is presently a corner), you would typically cut out the "half" bricks (ie every other course) to allow the extension wall to tie into the existing wall such that the bonding pattern matches and continues in the new wall. You would then use wall ties or starters for the inner leaf.

In both cases you should cut right though the outer leaf of the brickwork in the line of the cavity and insert a damp course (DPC) to prevent mositure tracking across and appearing as damp in the corner of the new extension. Ideally, you would cut out sufficient to allow an insualted DPC to be used to also prevent a "cold bridge" along the existing wall.

As you have correctly identified, you will also need cavity ties in the new wall.