First and foremost, there is a lingua franca in fairly common usage throughout Muunfel. Not everyone knows it, but there are usually enough people around that have at least a basic understanding for communication to happen eventually.
For a general idea of the different languages found among the peoples of Muunfel, I have considered some real-world analogs for some of them.
Elfkind: There are several regional dialects, but the elfish language is smooth, sibilant, and rhythmic like some romance languages (Spanish, Italian, Portuguese).
Faekind: Many fae are able to use a very low-energy glamour to speak whatever language they need to, but the fae tongue contains many compound sounds where words are shortened or combined with others on the fly (like the style of German with the sound of really smooth French).
Tamkind: The Solians speak a rolling language with a lot of hard or fricative phonemes (Arabic, Farsi). In the west, this is the second most common language in use among humans, as many of the folk living in the deserts of Rutan are descended from groups that interacted directly with Solians.
There are also several communities here and there that have developed and spread signed languages (”handspeak”, colloquially). In Rutan, sign is one of the official languages of the nation. A Braille-like system is also in use in many scholarly places, though it is not as common in the wilder areas of the continent yet because of the difficulty in spreading any print media to such locales.