Is it prescribed for the worshiper to recite a surah after Al-Fatiha, or is Al-Fatiha alone sufficient in all rak'ahs of the prayer, and is what he does by reciting a surah after Al-Fatiha in the first two rak'ahs and sufficing with Al-Fatiha in the latter two correct?

What you are doing — reciting a surah after Al-Fatiha in the first two rak'ahs and limiting yourself to Al-Fatiha in the remaining rak'ahs of the four-rak'ah prayer and the third rak'ah of Maghrib — is correct and in accordance with the Sunnah. However, if the congregant hears the Imam's recitation, he should not recite the surah with him, based on the Almighty's saying: ﴿And when the Qur'an is recited, then listen to it and pay attention that you may receive mercy.﴾