Amaya's in the database. It does mean "night rain" in Japanese. Amia was a Latinisation of
Amy used in baptismal and other formal records in the Middle Ages, and it stands to reason some could have also used Amya; but I don't think that's very relevant here.
Anissa's not in the database, but
Anisa is. There's also
Anise, and
Annis.
Alizé, or rather Alizée, was just brought up on December 3rd:
http://www.behindthename.com/bb/arcview.php?id=114287&board=gen.
Amar means "immortal" in Sanskrit, and Amari's quite likely a form of that. Alternatively, Amari could come from
Amara. (Note that
Amara could also be a feminine form of
Amar.)
I have no concrete evidence for Aleah, Aja, Alena, or Arely's origins, but I would suspect the same things you did for them.
Miranda