Great work! A couple of notes though:
Fána fáwë! Fána fáwë! A liquistëa heri!
fáwa is a word from very early in Tolkien’s life, later he uses losse pretty consistently.
A tári han i andúnë aireni!
aireni was likely replaced by †aire, pl. *airi “sea” and †airon, pl. *airondi “ocean”, and the modern equivalents ear, earon.
Ámen calë i ramyammë hí
This is the order “shine for us”, the original has the mere statement “light for us”, which would be cala men. The latest ending for “we” is -lme, -mme was at some point the regular suffix for “we” but was later revised to the dual “I and someone else” (Are you using Quetin i lambe Eldaiva, because it teaches the paradigm before this revision?). “Here” is sís/sisse/sinome, I”m not sure whether khĭn- as a conception survives.
Imíca i amba rembinë aldarion!
Amba means “up(wards), more”, “world” is ambar. The plural of alda is aldar, genitive aldaron, no need for an addidtional -i-.
Elentári! A Varda!
Semantically Gilthoniel “Star-kindler” is closer to Tintalle “kindeler” than Elentári.
Liquistië nát henduly' ar súlelya calima!
Usually the number suffix comes after the possessive suffixes: má → marya → maryat “her two hands”, so hen → hendelya → hendelyat.
Fána fáwë! Fána fáwë! Lirimmë len
fáwe and -mme again. Le, dative len is “you (plural)”, since Varda is only a single person, it should be lye, lyen.
Haiya nóressë han i airen.
airen again.
A elen' i anarvalta yénessë
-valta is a very early word, later we have -enca with the same sense. Since Anar has the stem Anár-, I would compound it as anárenca. Note that yén is an Elvish “long year (144 years)”, a seasonal year would be loa, locative loasse.
As calima má senen rérë nér,
I find as “with” somewhat problematic because AS > ar “and”, I would suggest ó.
Vailimë salquenórissë sí calimë ar liquistië
There is some evidence that when a noun is declined into a case, the adjective was doesn’t agree in number, so vailima salquenórissen.
Cenimmë telepta almalya hlápula!
-mme again. Hlápula is attested in Marcirya, but inn the PE22 paradigm it would be hlapuila, it’s up to you which paradigm you use.
Renimm' en, me 'n harë
-mme again. I don’t think en captures “still” well, I would suggest sinna, tensi. For me + i + hare I would suggest m’ i hare, since hare doesn’t start with a vowel to trigger i → in. “We, who dwell” is plural so I would suggest hare >> harir
Ilmalya i andúnë airenissë.
airen again, adjective agreement again, so andúna airissen. With the example elen síla lúmenna and caita mornie i falmalinnar, I would also consider the allative airinnar