Ideas....
Maybe we ought not to look at Tolkien's Elves at
all if we want to find any reflection of 'our' Faerie. They are altogether too perfect to be a representation of Faeries, too controlled and
moral. Tolkien's Elves are more like Men, or rather, like idealised Men.
In terms of relationships, Tolkien's Elves are sometimes like stiff, buttoned-up Victorians with high romantic ideals - I'm thinking of figures like Ruskin here, with the apocryphal tale of what happened after he saw his wife undressed - for Elves, romantic ideals are easily shattered. For Faeries, quite the opposite would be the case! Seemingly, it is only when Men arrive on the scene that passions start being stirred. It fascinates me
why Tolkien should write his Elves in such a way...
It is possibly in other areas of Tolkien's work that Faerie emerges. Dare I say that the Dwarves have a lot more in common with Faerie than do the Elves? They traditionally live underground (not all Elves do this, only some), and their realms are like whole other worlds, literally The Underworld. In common with Faerie, Dwarves keep their names secret, they also like to keep to themselves, and to upset a Dwarf is to make an enemy. As to the difference that Dwarves are mortal, they are also long-lived, and we cannot say that faeries are
always represented as immortal; there are stories of Faery deaths. The other main difference is that we often equate Faerie with beauty, but who is to say that Faeries are not little fellas with long beards?
Relationships between Elves/Dwarves were once good but now have declined, much as the relationship of Men/Faeries has declined. Any Men who consort with Faerie might be viewed suspiciously; they live on the margins. Eol was one Elf who lived in this way, preferring the mystery of the Forest to the society of Elves, and trading with and taking company from Dwarves; he is like the figure of the Mage who lives on the edges of the community, shunning the rules and forging relationships with Faeries.
Hobbits too can be more Faerie than Elves are; Faeries are often seen as small, and fond of humour and feasting. Gollum is like the tricksy side of Faeries. The Woses may be Faeries too. And I find Tom Bombadil and Goldberry would be more appropriate as the King and Queen of Faerie than any Elf; they remain slightly enigmatic yet familiar, otherworldly and unpredictable.
Just some ideas to stir into the pot...