The name fair folk is from Celtic mythology but every culture around the world has stories of the same thing, you may know them by the name fairy but I hate using that word because it gives the connotation that the fair folk are six inch tall women with butterfly wings in the vain of Tinkerbell. The actual faeries from mythology were frightening otherworldly horrors that kidnapped children and people to their realm either as a tithe to hell (a later Christian addition to the myth) or for slavery or worse things. The fair folk were called the fair folk because to call them by an uncomplimentary name would be a good way to bring about their wrath. In other cultures they are known by other names and may be even more malevolent, or more benevolent depending on the culture. The Norse called them the Alfar,the Greeks Daemons, the Persians the Peri, the Japanese Youkai, the Arabs the Djinn, and the Spanish and South Americans the Duende. In all cultures the story is more or less the same, the fair folk are spiritual supernatural creatures that live on another plane of existence or Otherworld. Their real appearance in mythology varied widely as they are spiritual beings and can basically look like anything they wish though most stay in one form.
To give you an idea of what the fair folk are the best interpretation I've seen period of the concept are the Daedra from the Elder Scrolls with their alien morality, Faustian pacts, many forms, dwelling in another dimension, and overall disregard for human life. Basically in my RP the alternate universe that the players are transported to is actually the Otherworld of legend. This would also make sense why a bunch of humans would be transported to this world. The fair folk become more powerful when humans are around do to their creativity and thus the main characters would be kidnapping victims trying to get home.
As for the characters, you know how I've been wanting to do another self insert for a while right? Well, I think that this story will be one too. Of course that doesn't exclude you from making some awesome NPCs but I've been wanting to do another SI for a while.