Yeah, Wondrous Tales is a piece of side content that comes out of Idyllshire so youll need to get there first before you can unlock it. A quick peak doesnt mention it being tied to completion of 3.0, but that is possible too. For now you can ignore it. As for the challenge log, all of the entries more or less stand on their own. For the most part you can complete whichever of them you like, in whichever order is convenient, and get your weekly rewards(with the obvious exceptions - for instance you cant kill 100 things with your chocobo if you havent killed 20 of them).

And like Eclipse said, the rewards for doing many of them are in the final tab of the log. The "Complete X Challenges" entries. For those entries the log counts every challenge you completed whether it was battle related, crafting related, gold saucer related, or whatever else. It counts them all, and you get the gil rewards every time you reach the next threshold.