I am not a stone mason expert, but you should have success attaching your cement board to the studs. The wall may not be a bearing wall but looks to have been built properly. I would screw the backer board to the studs, then apply the stone in accordance to the manufacturers specs. My father has a place similar to your situation and that is what they did. Think of it this way, you have studs hold the backer board in place, then the stone is built up and is supported by the backer board but mostly by the mortar. I can not tell what material is on there now, if it is sheetrock I would remove it. It would be fine to leave it and install the backer board over, you could also install the wire mesh to the drywall (if drywall) and build up your scratch coat then apply the veneer.
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