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Hardness is expressed as calcium carbonate equivalent: calcium multiplied by 2.497 and magnesium by 4.118, being the ratios of calcium carbonate's molar mass to each element's equivalent. Carbonate hardness is the part balanced by alkalinity and removable by lime; the remainder is non-carbonate and needs soda ash or ion exchange.
Hardness as CaCO3
Total hardness = Ca x 2.497 + Mg x 4.118
Split
Carbonate hardness = min(total hardness, alkalinity); non-carbonate = total - carbonate
Because the treatment differs. Carbonate hardness precipitates with lime alone; non-carbonate hardness needs soda ash, which is more expensive and adds sodium and sulphate to the treated water.
No, and there is some evidence of cardiovascular benefit. It is an aesthetic and economic issue: scale in pipes and heaters, and increased soap and detergent consumption.