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1. Can set the time by its self. Either via radio, or NTP across a network, or even as simple as a long lasting coin battery and computer clock chip. Doesn't need to be 100% accurate, just survive power outages and such.

This is known as a radio controlled clock or radio clock for short. Not to be confused with a clock radio

As tfabris started to say, the transmission frequency is normally either 60kHz or 77.5kHz in one of three similar formats (MSF, DCF or WWVB - there are others, these are the most common).

If the clock consists of only a radio controlled alarm clock chip and an LCD, a single AA battery or button cell will run the clock for a few years.