I don't think it dissolves completely. That sediment has to be cleaned out. I haven't done mine yet and it's been months. I don't see any issues so far.
Probably depends on which Kalk you’re using (some clump up more than others), how much Kalk and flow you’re running. Back when I ran one, I could go a year with Mississippi lime (about 2-3 cups a week) at just over 3 gallons a day. I had a couple bags of the brs brand that I tried but the stirrer would start to bog after a couple months or so.
i do not to move the unit from it's location; i siphon out as much kalk from directly from the bottom while trying not to turn it into a cloud, add my half cup of kalk, top her off, walk away.
takes me 5 minutes or so. i do this once per month, give or take.