do you have to be an engineer to craft anything?

Crafting and the engineer class have nothing to do with eachother.

Crafting is a mechanic in the game that anyone can do, in the early levels (lv10 you get the quest) you get some introduction into crafting. At the same beaver NPC you can buy a bunch of recipes for lv1, 5, 10, 15 crafting. Anything higher then lv15 at this moment is drops only.

Crafting specialisations use the same experience level as the 'general crafting' or 'food crafting', you can learn 1 specialisation at a time. Unlearning it results in losing any recipes you learned of that specialisation.

This might still be preferable.
Grinding a couple hours you might find a lv16/21 weapon recipe even though you're planning on accessories you might wanna use said weapon recipe to boost your exp through to the next point =)

As it stands we got Accessory, Weapons, Sub-Weapons, Cloth (Caster) Armor and Tech (Melee) Armor as specialisations. Next to the previously mentioned General Crafting.