Is it permissible to recite Al-Fatiha silently by mistake in the first rak'ah of Maghrib prayer, then repeat it aloud, and perform two prostrations of forgetfulness after the tasleem?

Your prayer is valid, and there is no blame upon you. Reciting Al-Fatiha is a pillar (rukn), and reciting aloud is a sunnah according to the majority of scholars, and obligatory for the Imam according to the Hanafis. Repeating Al-Fatiha to perform the sunnah of reciting aloud is correct. Regarding prostration of forgetfulness (sujud as-sahw) for this, there is a difference of opinion, and it is for recommendation (istihbab). Repeating Al-Fatiha does not invalidate the prayer, because it is a verbal pillar. Reciting aloud in a place where one should recite silently, or vice-versa, does not invalidate the prayer, nor does it require prostration of forgetfulness according to the Shafi'is, Al-Awza'i, and Ahmad. However, Malik, Ath-Thawri, Abu Hanifa, and Ishaq deem it obligatory.