Q: Where is Darien?
A: The Isthmus of Darien is now called the Isthmus of Panama. Balboa (whom Keats mixes up with Cortez) stood there to view the Pacific Ocean for the first time.
Q: What does Keats mean by "which bards in fealty to Apollo hold"?
A: He means that the bards hold those islands sacred to Apollo. OED defines fealty as "The obligation of fidelity on the part of a feudal tenant or vassal to his lord." Apollo was the Greek and Roman name for the god of the sun, who was also associated with music, art, the nine Muses.
Q: What does demesne mean, and why is its spelling so weird?
A: Demesne means "possession." You can look up it's etymology in the OED, and you'll see it's related to the word domain. That's just the way the word is spelled, but these days, people more often use the word domain.