Why do clerics still worship things and fill that divine niche?
Because the human (or demihuman) mind still needs to cling to the notion that they aren't alone, that some higher power is protecting them, or that life itself has a purpose. Just like in the real world.
Why do they have auras of good and evil etc?
A god-less cleric has an aura based on their alignment (i.e. their conviction). A god-ful (

) cleric has an aura based on his religion (so a LE cleric of the Silver Flame has a LG aura).
Why can they turn undead?
Because they're very good at wielding positive or negative energy, due to their religion's training (even god-less clerics must have faith in SOMETHING, like an ideal, and have trained to be clerics).
Why do they have holy symbols?
Because they need a focus for their faith, an anchor of sorts. In the case of god-less clerics, it can be any item that has a personal significance to him.
Why do they have a diety favored weapon?
Because the religion says so. No one knows if the god really exists, and if he do, if he wields such a weapon. The Silver Flame, for instance, is not an anthropomorphic deity, but still has the longbow as a favored weapon (representing the light rays of the Flame). Keith Baker will be writing a Dragonshard on god-less clerics and what weapons they favor.
The Ring of Syberys isn't just a bunch of rocks. It's the remnants of Syberys, one of the progenitor-wyrms that gave birth to the world itself. The ring is made up of dragonshards, magical stones that can be used to make several special items. And it is theorized that the Ring of Syberys isn't just the source of these cleric's magic, but of ALL magic, arcane or divine.