You can probably start cooking it to gain skill at level 0, as long as you get advanced imagery from the Cooking Guild while you're cooking.
Note that you may break many crystals and lose ingredients in the process, but you'll still be gaining cooking skill even when the synthesis doesn't work.
The number 7 by the name of the item is when you max out your skill for that item. You cannot gain skill by cooking this beyond Cooking level 7.
BST get a job ability at Lv23 called Call Beast. It summons an animal called [something] Familiar, and acts like a tamed beast. The ability has a five minute recast timer, and uses on jug of broth to call the familiar. The HQ versions have higher level requirements, but call stronger monsters that usually have their own names ^_^