When a pilot ejects, what happens to the ejection seat? Does the pilot stay in the seat until he lands, or does it get disconnected from the pilot somehow?
It depends on the seat. Most modern seats, including the ACES II system common in US Fighter Jets, fall away from the pilot at a pre-determined altitude. [src]
Generally, according to that link, this occurs at just over 100-200 feet above ejection height. However, if you eject at high altitude, such as Captain Scott O'Grady did (26,000 ft), the seat will fall away on a sensor (either 10,000 or 18,000 feet, I don't recall which). The chute may open automatically, or if it is not set to at that height, you can then pull the chute manually, or wait until its set height to open.