For the US, it's on a state-by-state basis but rescue is usually free as long as it's a true emergency and you weren't blatantly reckless to begin with.
For other parts of the world, you might get a bill to recover the cost of rescue. But in most cases it's still usually free.
(Medical care once you get back to civilization is a different story.)
Undefined. But at zero cost in every case I know of, in a multitude of countries. Be it a simple policeman driving into the middle of the desert to help a cyclist, to a complex joint, multinational, civil-military operation in the middle of the ocean, with aircraft and the rerouting of container ships.
This isn't true everywhere. E.g. in the alps you might be billed for rescue, particularly if you're not injured or in a medical emergency. That said, SAR insurance is cheap. Many alpinist associations and the likes offer it as part of their membership, which is often less than 100€/yr. There's no reason not to have it if you're going out into the mountains.
