In the beginning of Eragon, Fäolin was described in the following passage, though which elf he was isn't certain:
"On the first horse was an elf with pointed ears and elegantly slanted eyebrows. His build was slim but strong, like a rapier. A powerful bow was slung on his back. A sword pressed against his side opposite a quiver of arrows fletched with swan feathers. The last rider had the same fair face and angled features as the other. He carried a long spear in his right hand and a white dagger at his belt. A helm of extraordinary craftsmanship, wrought with amber and gold, rested on his head."
Relationship with Arya
In Brisingr, Arya said that she and Fäolin were kindred spirits even though he was older than her. Decades after Arya became the elven ambassador, Fäolin volunteered to accompany Arya wherever she was sent. At first, Arya refused, but he was very convincing and her mother liked the idea.
For over twenty years, they traveled together as the only "immortals to walk among the short lived races". Arya never directly says that she loved Fäolin but it seems clear that they were at least close friends. It is not as clear is if she loved him or was merely a very close friend. It is known that Fäolin created one of her favorite flowers (A Black Morning Glory) for her using magic and that this preserved blossom was kept in her quarters, next to a Fairth of an elf who may have been Fäolin.
In the third book, while Eragon and Arya are alone, Arya reveals that she and Fäolin were only close friends but she fails to elaborate. This causes the friendship between her and Eragon to strengthen, particularly when Eragon creates a flower for her.
Paolini later revealed that they indeed had a romantic relationship.
In the GBA Eragon game, Fäolin appears (very) briefly as a playable character when Arya and her guardians attempt to escape the Urgal ambush. His specialty is the sword, he is otherwise unremarkable. Although likely non-canon, his hair is red.