This is a common expression when referring to the water from your household plumbing, the tap-water. For example, "We have hard water in our house, so my pipes got clogged!" It is not commonly used to refer to bottled water. You would call bottled water with high mineral content "mineral water."

No, it's not a common expression (at least in the US). If we talk about having hard water it is usually about our tap water in the house (or city). My parents live in the mountains and use well water, so they have hard water and have to use a softener in their water because the minerals can build up in the pipes. I think we just assume that a bottle of water we buy is soft (unless it is specifically "mineral" water)