Answered by Shaykh Faraz Rabbani
I understand that it is not wajib to recite al fatiha in the last two rakahs of a four rakah fard prayer. Does this apply irrespective of whether one is the imam or praying by oneself? Also, does this apply to the third rakah of maghrib?
This applies to everyone, after the first 2 rakats of any fard prayer, if one did the wajib recitation in the first two rakats. This included the final rakat of Maghrib.
It is superior, however, to recite the Fatiha. See answer below
The Obligatory Prayer:
Not reciting the Fatiha in the final two rakats
What is the ruling of reciting the Fatiha in the final two rakats of prayer?
In the Hanafi school, it is not necessary (wajib) to recite the Fatiha in the third and fourth rakats of the prayer. Rather, it is a
sunna to recite the Fatiha. The sunna is also fulfilled by saying the tasbihs (=saying SubhanAllah) three times.
This has been transmitted, by Ibn Abi Shayba in his Musannaf and others, from Ali, Abd Allah ibn Mas`ud, Ibrahim al-Nakha`I, and others, with sound chains of transmitters. Details may be found in I`la’ al-Sunan.
Abu Ishaq reported from both Ali and Abd Allah [ibn Mas`ud] that they said, “Recite in the first two, and do tasbihs in the last two.” (Musannaf Ibn Abi Shayba) That is, it is permitted to do so.
Reciting the Fatiha is Superior
Note, however, that reciting the Fatiha is superior, even though both are permitted.
In Non-Obligatory (Fard) Prayers One Needs to Recite the Fatiha in all Rakats
Note, too, that this is only in obligatory prayers. In one’s witr, sunnah, and voluntary (nafl) prayers, it is necessary (wajib) to recite in every rakat. [Ibn Abidin, Radd al-Muhtar]
And Allah alone gives success.