Does the emission of semen through massage, without feeling any desire or erection, invalidate the fast?

Your fast is valid, because the discharge occurred without lust or intention. If a man rubs his penis due to an itch or similar reason and discharges, his fast is not broken according to the more correct opinion, because it results from a permissible interaction. By analogy, rubbing or massaging the back does not break the fast. As for ghusl (definition) (ritual bath), the Shafi'is have made it obligatory, while the majority opinion is against it.