The only purpose-driven Endless is Sphene. She is hardwired to preserve Living Memory at all costs and cannot directly contradict that directive, but the others are not. If the AI modeling Cahcuia concluded that she would tire of eternal "life" as an Endless knowing the cost, she would then be compelled to find a way to shut down Living Memory... which is exactly what happened.
Other than Sphene the Endless have no purpose; they're just images acting out behaviors modeled on data. Living Memory is itself just a comforting lie about "eternal life," which is stripped away when we shut down the Terminals running it. Even Sphene's behavior is modeled on personality data (memories) from the Storm Surge era Sphene, albeit modified to have her love and compassion amplified by Preservation. The only time we talk to "Sphene" as her own independent self is in the moments after defeating her Queen Eternal form, as she is still shorn of Storm Surge Sphene's memories; and she concludes she never should have been created. (Harsh.)
There's a fortune teller in one of Solution Nine's buildings, directly behind the Neon Stein mini-aetheryte warp point. It's the building with the neon Yans on the outside. All the clerk says is that they're busy and will be for a long while, and to check back later.