No, when we have a power outage we say power outage, blackout, power failure or the electricity is down. If we say the 'lights are out' it could be due to many reasons such as a blown fuse or somebody turning the switch off.

yes, like "the lights are out on every street."

They can or can not mean the same thing. Lights can go out for different reasons, say for example, a burnt bulb. Power outage can be one reason too. So, if a power outage is the reason, they mean the same, else they dont mean the same. Hope this helps. :)

Just what Kevin said.

Yes. When the lights are off, the switches have each been placed to the off position. If none can come on, the lights are out - along with most everything (which does not need to be added.)