Parity codes (of which fountains are a subset) are based on XOR, making them much faster than RS's Galois field arithmetic. Parity codes are generally less efficient than RS (you have to receive 5-10% extra data to recover), but the net performance is better due to faster decoding.
jsyedidia explained the benefits of ratelessness, so I won't repeat it.
What you said is correct but just to be nit-picky: parity codes constitute Galois Field arithmetic as well. XOR is the addition operation of polynomials in GF(2^n).
jsyedidia explained the benefits of ratelessness, so I won't repeat it.