Yes and No. You do have to spam-craft to level them up to get what you want out of them. However, you can teach them alternative items to craft if the level is appropriate to their skill level.
Seems that they will indeed die and vanish. I had to craft another stattion and assign a new survivor.
In the end, just make sure they have plenty of mats and food to last a long while.
Side note: The recipes you see bu can no tcraf are things above their current skill level. as they skill up hose will become available.