The lain intended here is this one, from √LEK "loose, unbind, let, permit", so no issues with using this. Rain "free, unconstrained", on the other hand, is essentially no different from rain "erratic wandering"; in other words using this would yield "wandering spirit", which is not quite what was intended.
Faer is the right word for the spirit of a non-living creature. Faerlain, too, seems correctly formed.
A word on the suggested Ferrein: as discussed in previous threads, I don't think [ae] would reduce in an initial stressed syllable; furthermore, [ei] can only ever exist in non-final syllables, whereas [ai] is its counterpart in final positions. So faer + rain > Faerrain; or possibly Faerain, if we take Aerandir as an example of [rr] reducing to simplify a superheavy syllable (though I should note that Faerain would look more like an embodied spirit, fae ⪤ Q. fëa, rather than a non-living thing).