Side quests can only be done once. It doesn't matter if you change classes.

Currently, none of the databases are updated with the new recipes except the one under the Synthesis tab on the Lodestone site. Unfortunately, the recipes don't show stats.

You'll have to use another website for stats and the lodestone website for recipes. I suggest using this one for stats since it has an easy to read layout:

http://www.mooglebox.com/