How about Naias or Nais?
Doubt it really matters. It's always best to go with the most common spelling in English so I would go with Naiad.
I don't think it is Morrigan, since Persona PSP uses モーリアン for that.
They are sort of the same deity. But it would probably be best to either call her Morgana or Morgan Le Fay to keep her separate from the Morrigan/Morrigu triune.
Since KMT1's demon is a horse and is spelled as プルーシー; and KMT2's demon is an elephant and is spelled as プルシキ.
Maybe keep Purski for KMT2 and let KMT1 use Pulukisi?
Purski isn't anything. Pulukisi is the elephant since it means "pole elephant" in the Newar language. Now that you mention that the kanji is different for those two demons, I'm inclined to agree with Djinn that the demon in KMT1 is Kimpurusha. The Kimpurusha has a human head and horse body. They are related to the Kinnara who have horse heads and human bodies.
Persona 2 Innocent Sin and Eternal Punishment use アポロ for Apollo, but this game uses アポロン (Apollon).
Oh, either is fine. It's just that since this game has another demon called Apollyon, it would probably be better to call him Apollo instead of Apollon.
As for your MT1 list:
Just some spelling corrections and repeats:
アピペ - Apipe = Apep
タランテラ - Tarantella = Tarantula
ファライ - Foraii = Erinys
ナアス - Naas = Naiad
ギルタブ – Girtablilu - I think this one is mostly okay but Google Books seems to be directing more hits for the proper name of this being with the Girtablulu spelling. Girtablilu just refers to the species.
プルーシー - Pulukisi = Kimpurusha
And everything else is fine.
When translating the names you don't need to be 100% accurate. If the spelling is awkward in English or if the version of the spelling is used less oftern, you are better off translating it into a more common variation.
Stab in the dark guess about Skotinka. If it means little cow in Russian, then maybe the folktale called Burenushka the Little Red Cow would fit? Stonka is red and since it's in the Majuu clan, it doesn't necessarily mean that Stonka must be evil and Burenushka is a good cow.