Fairies, demons, elves, angels, etc do exist on the astral plane. They can exist on the physical plane but they dont become physical. Most ghost sitings arn't ghosts at all but somthing from the astral plane. In my teaching, all things that live on the astral plane are referred to as spirits.
You can contact them by become astrall attuned (thats the most direct way, because its like walking up to a spirit and starting a coversation)But there are many ways use to contact spirits with out being astrally attuned, such as allowing the spirit to control you body. Often if you just call out for a spirit it will hear you even if you cant hear what it says back.
Yes most stories do have some truth to them, though in this case it is fully in the astral that these beings exist they can have a profound effect on the things in this world but in subtle ways.
To speak with such beings requires the ability to see and work with the astral, unless you take up channeling.
Link to Channeling,
Link to info on Astral Projection.