Kalkwasser adds equal parts of ca and alk. So, yeah in theory it should be enough especially for a smaller system. Is the kalk dispenser the tunze osmolator add-on gizmo? If so, be careful not to pu too much kalk in there so undesolved kalk is not going into the system. The effluent should be clear liquid. Also you want a small air gap were the tube enters the sump to prevent a siphon, but don't have too much as aerating it would cause carbonate to precipitate out.
If you decide to continue the A&B dosing, I would add equal parts of each at the same time to the tank...like within minutes of each other. and be sure to add it at a good mixing point. For example, where your overflow discharges into the sump is normally a good spot.
With kH only in the 7 dkH range, and considering how much your dosing I would agree that the precipiate is likely carbonate. I would expect a much higher dkH. Also what are your magnesium levels? Do you ever add any?