Hide-boxing this because though I see you are Lv80 I don't want to presume you've done 5.X.
The black-masked underling Ascians are, presumably, just normal Echo-users that sided with the Ascians and were granted greater knowledge of how to wield the Echo.
Thanks to the Echo all Ascians can cheat physical death, but killing them on a metaphysical level is much more difficult (the whole "Blade of Light" + soul container bit), and they also have a way around that - jumping into an interstitial rift between the worlds via a Dark Crystal, though that takes a little bit of preparation to use. The only difference is the black-masked underlings lack the power to possess a living host, so they must possess corpses; Dark Crystals also appear to be at a premium, and so they do not make use of them.
The unsundered Ascians are simply using the power of the Echo to unnaturally extend their lifespans. It's implied in one of the short stories that without memory crystals to keep their minds together the unsundered would have lost their identities long ago; indeed, both Elidibus and Lahabrea are no longer who they once were (Lahabrea having given himself over to a lust for destruction and Elidibus abandoning his humanity in favor of his directives as a primal) and only Emet-Selch still bears a resemblance to who he was in the days of Amaurot (due to regularly using his soul crystal and taking long "naps" besides).
The sundered Ascians you meet throughout the story are not the original, but a reincarnation raised up to their former office via memory crystals created by the unsundered Ascians. (Though they don't need to be a reincarnation of the former Ascian, those are preferable.) We don't see 2+ sundered Ascians because the unsundered only raise up one sundered at a time; after being freed (to an extent) in the last tier of Eden Mitron implies this might be done so if a sundered Ascian is killed or otherwise disposed of they can just go grab another fragment and raise it up to fill the slot.
Addendum: sundered Ascians (former Convocation seat holders) are no different from ordinary mortals before being restored to their office by the unsundered. Their powers and memories are restored via crystals containing the identities of the former Convocation seat holders as remembered by the unsundered.