1. Fish need to be fished up with a rod and bait. I have no idea what that fish or quest is though.

2. You craft by using crystals. Just go to your inventory and use a crystal like you would use an item. Then you put the appropriate materials in the boxes that you wish to synthesize together. Each synthesis recipe has a level, and high level ones will be out of your reach until you skill up (you skill up by crafting). There's no quest you need to do before you craft. As long as you have the right materials you can attempt any recipe.

Crafts - FFXIclopedia, the Final Fantasy XI wiki - Characters, items, jobs, and more will show you all the crafts along with the recipe's and appropriate level caps for the recipe. That should help you get started.