Did he know about the Quileute tribe before Irina went and told them, or did he have that information stored away but not processed yet? I'm guessing it's the latter, since he immediately acted when Irina requested their help.

I think there's enough clues in the text that I can just say outright: yeah, Aro had werewolf-related information stored but not processed before the story began. Irina a) prompted him to process it and b) informed him that it was relevant in the present.

the Cullen coven believed the gene to be dead (they did, right?)

No. They believed there were no active werewolves (and they were right until Bella went in and shook hands with everybody), but had no reason to believe that the gene had died out.