First, check that the wall you plan to frame against is proper; just knock a little and ensure that it is a masonry wall, like lightweight concrete as you assumed. Patching is mostly cosmetic, knock off all loose material and repair with a repair mortar (ask at Beijer, for example) or maybe just wall filler if the damage is not too deep.
Then, as you said, drill, plug, and screw (the packaging usually states what size screw and drill bit to use), or alternatively, nail the plug to the frame. And, of course, not too close to the edge, so you don't risk more cracks.
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