The US, Russia, Great Britain, France, China and (recently) India have nuclear submarines.
From Wikipedia: Today, six countries deploy some form of nuclear-powered strategic submarines: the United States, Russia, France, the United Kingdom, People's Republic of China, and India Several other countries, including Argentina and Brazil, have ongoing projects in different phases to build nuclear-powered submarines.
The PLA navy has more than 225,000 personnel and is thought to have as many as 70 submarines, 10 of them nuclear-powered
USA has the most nuclear submarines
Argentina had diesel-electric submarines while the British had nuclear-powered submarines.
Reactors power submarines and many surface ships. Nuclear weapons.
Nuclear submarines are powered by a nuclear reactor and they are completely independent of air, so there is no need to surface frequently.
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.