The crafting log is good, yes. I also recommend working on the Ishgard Restoration Project, and the Diadem.

When it comes to crafting, what I normally do is farm a lot of mats for the easiest, highest level crafting recipe at my disposal, then I Quick Synthesize the heck outta of it.

As for gathering being automatic, whenever you select a gathering node, you should see a box in the lower-left corner. Click on that before choosing the mat you wish to gather, and it will automatically gather them for you. I hope this helps, and I wish you the best of luck!