Yes, I add salt at the time that I strain the whey after brining the cheese. That way it is ready to go for the next one, right out of the fridge. I also figure that the salt will dissolve better in the room temp brine than it would fresh out of the fridge.
I've never added CaCl to it. My cheese are all raw milk, so I don't use CaCl, unless making for a class with pasturized milk.