I was under the assumption that the Calm lasts 10 years.

LoM's got it for your second question.

Anima was Seymour's mother, who became an aeon in order to protect Seymour from being harassed. The pilgrimage only requires journeying to Besaid, Kilika, Djose, Macalania and Bevelle. Then the summoner has proven their worth and command over aeons and can meet up with Yunalesca and get the final aeon.