Elena was the only spirit without a “spirit” indicator on the world map, and her challenges are hard. Is it necessary to bring her to the Everdoor in order to finish the game?

Not sure about the exact numbers, but I think you can "end" the game after 9 released spirits. Elena and Buck are likely the last ones you'll get, and Buck can't be released at all.

That said, doing Buck's questline unlocks an extra ability that makes Elena's challenges a lot easier.