Yes if your water doesn't have a high hardness level. If you have hard water then it should have enough calcium. If not you can buy supplements of various sorts to help increase the amount.
Most of them will say they are supplements and contain calcium, calcium carbonate and some will have iodine in them. I have Kent ZOE Freshwater supplement.
Yes it will harden your water but any kind of calcium you use will harden your water. It depends on a lot of factors though on how much it hardens the water. I'm not sure if you can use saltwater specific calcium supplements like that in freshwater though.