Turning water off to house for a vacation, does furnace need to go off as well?
If the water is shut, should water level drop, e.g. if an outside faucet were turned on, it's likely a water heater or boiler would be damaged.

If plumbing is sound, I'd not shut the water for just one week in summer, since it's unlikely pipes would freeze. For a long-term winter vacation, if turning off heat, you'd need to drain the plumbing, dish- and clothes-washer, flush toilets, put potable antifreeze in drains, etc.