Is the Maghrib prayer valid if the Imam recited Al-Fatihah silently in the first rak'ah, then recited it and a surah aloud after rising from rukoo' upon being prompted by the worshippers, and then completed the prayer with sujud as-sahw (prostration of forgetfulness)?

The Imam should have continued his prayer without repeating the recitation or bowing, and then performed the prostration of forgetfulness (Sujud al-Sahw) to compensate for the omission of the Sunnah of vocalizing. Since he repeated the recitation and bowing out of ignorance, his prayer is valid, and he must perform the prostration of forgetfulness. However, if he did so knowing that such an addition is forbidden, his prayer would be invalidated, as would the prayer of anyone who followed him while aware of that fact.