With water as low as 3 - 5 grains per gallon, you should have practically no calcium deposits. As for iron, .03 is practically non existant. Yes it can stain, but it's certainly not bad.
You said your water specialist installed a filter with Calcite/MC-10 media in it. The only Calcite I'm familiar with is a PH correction media. It has nothing to do with removing iron. However it could add to your hardness somewhat.
Putting a whole house filter in after your water heater might be a bad idea. I'm not sure it can stand the heat for long. By the way, these things are not really whole house filters. They are one faucet filters. This is demonstrated by the size of it and your actual Calcite filter.
I would have some more testing done to see what your actual PH is before the Calcite filter or any others for that matter.