Tap water with lots of dissolved limestone is hard. If the calcium ions are replaced with sodium ions it is said to be soft. To determine if your tap water is hard, you can test it by using tincture of green soap. The softer the water, the more the foam. See the attached link.

You never know that tap water or well water is safe unless it has been lab tested. In wells especially this should be done annually.

Definitely Tap Water.

you can tap tap

No, it isn't faster, tap water freezes just at the same temperature as tap water