Summons in X have a lot of setting-specific metaphysics attached to them, but you are correct on both counts. (Aeons are dreams of the Fayth, with whom summoners need a contract to summon their associated aeon. Though Anima as an aeon never speaks, her Fayth does so to exposit Seymour's backstory and forge a contract with Yuna, and Seymour addresses Anima as if she were his mother if you summon her against Seymour Omnis.)
The idea of Anima being linked to Fandaniel was fielded before, though I brushed it off due to his and Seymour's dispositions being wildly different. Knowing there's a character related to Fandaniel whose name was important enough to be redacted, though, now I can't help but wonder...