Monitor LCDs can't actually go below 30 Hz, they decay, too.
Yes refresh rate matters. Even while not playing games. Unless you live in an area with prohibitable energy costs 120 or 144hz makes everything better. More accurate mouse movements. Easier to drag and drop. Easier to navigate GUI's in general. Just make sure you have a good mouse to match.
Not for majority of the people.
Note, use 120Hz (or less) desktop for nvidia, otherwise it keeps the hardware in a power-eating state. Then choose "max gaming refresh" in 3D settings.