Nuclear submarines are powered by a nuclear reactor and they are completely independent of air, so there is no need to surface frequently.
USA has the most nuclear submarines
Argentina had diesel-electric submarines while the British had nuclear-powered submarines.
A number of nuclear submarines sank, and the circumstances vary from accident to accident. Wikipedia has a list, and by going there and entering "List of sunken nuclear submarines" you can review that list.
The US, Russia, Great Britain, France, China and (recently) India have nuclear submarines.
Just like diesel submarines travel underwater, but for much longer periods as the nuclear engine does not consume the oxygen in the air. The older diesel submarines were limited to running on batteries or using a schnorkel to get air for the engines when underwater, so usually they traveled on the surface like regular ships only submerging to prepare for an attack with torpedoes on passing enemy ships. The nuclear submarines can practically travel underwater forever, until they need to be resupplied with food for the crew.
Yes, nuclear submarines generate nuclear power. There is a nuclear reactor on board (hence the tern nuclear submarine) which creates steam to drive the main engines to turn the screw(s).
They made aircraft because nuclear submarines had not yet been invented.
As regards military submarines meant as warships, the Russians built the submarines with the deepest diving capability, but U.S. submarines generally make less noise.
Nuclear Energy
The PLA navy has more than 225,000 personnel and is thought to have as many as 70 submarines, 10 of them nuclear-powered
No - all submarines, be it nuclear or diesel-electric, use diesel fuel, either for primary engines (DE) or backup generator (nuclear).