You normally grow fuchsia from cuttings although certain species plants are grown from seed I have done this myself with moderate success breeders also use seeds for trying to make new types. The seeds do remain in the pod after the flowering has done.

We had this question last year - turns out that, although they form seedpods, most of the pods don't actually have any seeds in them, and even if you find a few, they don't come true, meaning you don't know what you'll get. The pods are edible, though not terribly tasty, apparently.