It's really good to know I can participate in these discussions, thanks! I don't think I've listened to any of the lessons, but I've been reading some of the forum discussions around it.
What I wanted to share is that I have The Peoples of Middle-earth, and I can confirm that what Steven R and Lincoln Alpern posted is basically right.
Tolkien did reuse some other Elvish names, and decided that there are 2 named Gelmirs and 2 Galdors, for example. But he decided that those are simple names that could have been repeated, while Glorfindel is a longer and more unique name that wouldn't be reused.
In-universe, Glorfindel was restored to life before the end of the First Age, less than 35 years after he had died. He was sent back to Middle-earth specially as a messenger of the Valar, to help out Gil-galad and Elrond and the Elves fighting against Sauron. He had always been both physically and spiritually potent and became more powerful as a direct result of sacrificing himself for a good cause, and was experienced in fighting against demons and other monsters of Morgoth. That's why, in Corey's words, the Nazgul flee from him "like scared children." I imagine it's possible the Valar put special blessings on him as well, to prepare him for this role. I assume that he went back to Valinor along with Gandalf -- I don't imagine he'd want to stay in Middle-earth after all the other Noldor sailed West.
He apparently went East on a Numenorean ship. That raises the possibility that other Elves could have taken the same route back to Middle-earth, but apparently the Valar didn't normally allow re-incarnated Elves to leave the West. I don't know the reason for that, but Glorfindel, Beren, and Luthien were the only people to do so after dying. Even Avari whose whole families were in Middle-earth couldn't go back.
As for the other Elves, Tolkien didn't mention the fate of many by name. But he did write down the general way that the Valar deal with dead Elves, and how they're restored to life. Much of it was written before the Glorfindel text, which was one of the last things Tolkien ever wrote.
In short, Eru commanded the Valar that they have a duty to restore dead Elves to life, if they fulfill certain conditions: They have to willingly come to the Halls of Mandos, instead of choosing to stay in Middle-earth as ghosts; They have to wait an unspecified length of time, and accept teaching to learn from their mistakes and become wiser; If they did anything wicked, or rebelled against the Valar, they have to repent and go through a purgatorial "correction" (which they forget afterwards); They can't have any malice towards anyone who's alive (maybe not including Orcs and the like?); They can't be a member of a sexual threesome if the other two people in the threesome are alive (like Finwe, Miriel, and Indis); And they have to be willing to come back to life. The Valar build them a new body of the same age as the one they lost, so adults come back as adults.
Given that, I think it's likely that most dead Elves were restored to life. Tolkien didn't say how long they wait. Children are brought back very quickly, but some Elves have to wait "long", especially if it takes them a long time to repent of something bad they did. I imagine that nobody waits in Mandos longer than Morgoth did (2874.6 Sun years), unless they're so unrepentant that Mandos gives up on them and keeps them there.