If a population was immortal do you think their languages would evolve? Does it depend on other factors?
That's a question that I'm kind of having to deal with myself, since the Fae are ... well very long lived at least, and living in a world where time is weird. And after that, I'll move onto Celestial, Infernal, and Abyssal, which are spoken by genuinely immortal beings.
It really depends on the nature of immortality. I have to assume that these immortals still experience time in some way (otherwise communication through human-like language wouldn't make sense), so I imagine that their language would just change more slowly. There are forces other than imperfect child acquisition that can change a language. Without the generational transmission, changes would probably result more from a need to distinguish themselves as a social group, or from adopting new words or variations that have become fashionable. They also may be in contact with other beings, including mortals, that they'll borrow words from Or they might straight up forget things and have to re-invent it.
For the Fae, I decided that they're not entirely immortal and they can have children, so their language develops more or less naturally, just more slowly than human or even Material Plane Elven languages.
For the Celestial family, I think there are two main drivers of change. The Infernal speakers (devils), will probably have some more naturalistic changes because they'll be closer to the Material Plane races in some ways. Celestial will be much more conservative, but they'll also be influenced. Both with have extensive contact with the Fae, for reasons that will become apparent.
But the other force will just be social distinction. I will flesh this out on stream, but one thought I have is that many of the changes in Celestial will actually be deliberate reactions to changes in Infernal to distinguish themselves. So if the Infernals have lenition, Celestials might develop fortition as a counter. You might have some asura/daeva* stuff going on, where they choose opposing meanings for words relating to morality an ethics. I'll have to see how that works out.
Abyssal speakers (demons) are gonna be different, though. They're immortal, sure, but as the embodiment of chaos, I imagine they'd go absolutely wild with innovation, especially in the constant social turmoil of the Abyss, where another demon could conquer the whole thing tomorrow! I have a lot of worldbuilding questions to answer about the Abyss.
But I guess long story short, the language of immortals can still change due to all kinds of social forces. It'll probably just be more conservative. But... if you're writing immortal beings, also keep in mind their environment and their natural tendencies. Tolkien's Elves are fully immortal, but they have children and had a bunch of ethnic splits, so they have a full-on language family. Your incorporeal spirits that have perfect memory and only respond to speech to do magic might have one completely static language that mages have to learn by rote to get their spells to work. It all depends on the story.