(Refer to what are Pillars and Wajibs in Solah.)
(1) The opinions of Mazhab Syafie, Hanbali, Maliki = Yes, it is a Pillar.
Based on this [Sahih al-Bukhari 756]: From Ubadah bin al-Somit RA, the Prophet PBUH said:
لاَ صَلاَةَ لِمَنْ لَمْ يَقْرَأْ بِفَاتِحَةِ الكِتَابِ
"Whoever does not recite Fatihah al-Kitab (Al-Fatihah) in his prayer, his prayer is invalid."
Praying alone:
If a person praying alone does not recite Al-Fatihah on purpose, then his Solah is invalid.
If a person forgot to recite Al-Fatihah, then only the rakaat which he forgot becomes invalid.
Eg. He realized that his first raka'at becomes invalid. His "second" raka'at now becomes his first raka'at w/o the first tahiyat. Meaning he repeats the first raka'at again. Before ending the solah, do "sujud sahwi" before giving "Salam".
Eg. He realized that his 2nd raka'at becomes invalid. Do not do the 1st Tahiyat yet. Stand up and do the 2nd rakaat again with the 1st tahiyat. At the end, do "sujud sahwi" before giving "Salam".
Eg. He realized that his 3rd raka'at becomes invalid. Stand up and repeat the 3rd raka'at. At the end, do "sujud sahwi" before giving "Salam".
Eg. He realized that his last raka'at becomes invalid. Do not do the final Tahiyat yet. Stand up again to do the final Raka'at w/tahiyat and do a "sujud sahwi" before giving "Salam"
(2) The opinion of Hanafi Mazhab = Not a pillar (but wajib)
Based on [Quran 73:20]
فَٱقْرَءُوا۟ مَا تَيَسَّرَ مِنَ ٱلْقُرْءَانِ ۚ
"So recite ˹in prayer˺ whatever is easy from the Quran"
For them, reciting Al-Fatihah is "wajib" but not a pillar of Solah. Meaning if someone forgot to recite Al-Fatihah, the prayer is still valid. However he need to do the "sujud sahwi" before the "salam" and do not need to repeat the Raka'at that he did not recite Al-Fatihah.
(1) Imam recites the Fatihah loudly "jahar"
Mazhab Hanafi, Maliki, Hanbali: "Makmum" do not need to recite Al-Fatihah since the “Imam” is reciting Al-Fatihah aloud on behalf of them. Makmum needs to be silent and listen to the Imam's recitation of Al-Fatihah and Quran after that.
Mazhab As-Shafie: Everyone needs to recite Al-Fatihah.
If a person forgot to recite Al-Fatihah behind an Imam in a raka'at where the imam recites the Fatihah loudly, then there is no effect on his prayer according all mazhab except Syafie i.e. that raka'at is invalid (see below on what to do).
(2) Imam recites the Fatihah silently "sir"
Mazhab Hanafi: Makmum do not need to recite Fatihah
Mazhab Maliki, Syafie, Hanbali: Makmum need to recite Fatihah
- If the makmum forgot to recite Al-Fatihah in that raka'at, then that raka'at is invalid.
(3) Making up for an invalid raka'at
After the imam gave his Salam, he must not give salam but stand up again to make up for the missed invalid Raka'at. He do a "Tahiyat" again on his own and do a "sujud sahwi" before giving salam.
Only Mazhab Hanafi said that prayers whether "jahar" or "sir" is not required to recite Al-Fatihah for the makmum following an Imam.
(1) What if a person enters late into a congregation prayer while the Imam is at the end of his Surah recitation (eg. in the 3rd Raka'ah) and the imam immediately ruku'. This late comer has not enough time to complete his own Fatihah recitation.
-> In this case, he just recite whatever he could of Al-Fatihah and when the Imam goes to rukuk, he has to stop his recitation and do rukuk. Meaning his Al-Fatihah is incomplete. There is no need for him to do "sujud sahwi" at the end because he did not start together with the imam at the beginning of Takbiratul Ihram.
This is based on the dalil: "So recite ˹in prayer˺ whatever is easy from the Quran" [Quran 73:20]
(2) What if an imam recites Al-Fatihah in a quick pace (eg. in "sir" prayer) and does his rukuk while a makmum who started the prayer together with the Imam since the beginning has not finished his own recitation?
-> The slow Makmum will need to hurry up to complete his recitation while the Imam is still at the Ruku' position. He quickens his recitation even though he is unable to stick to all the tajwid rulings such as 6 harakat.
This is again based on the same dalil: "So recite ˹in prayer˺ whatever is easy from the Quran" [Quran 73:20].
This dalil overwrites the dalil of reciting Quran with "tartil" (tajwid) in Surah Al-Muzammil ayah 4 " .. and recite the Quran with tartil (in a measured way)".
(3) What if a makmum who begins together with the imam, has no time to catch up with the imam as the imam is about to stand up after ruku'. His Al-Fatihah is incomplete due to several reasons, eg. perpetual coughing, yawning, sneezing, he forgot to recite Fatihah, day dreaming, etc.
-> After the Imam has given the salam, this makmum need to stand up (w/o giving salam) to "make up" for the missed raka'at since he did not complete reciting Al-Fatihah for that raka'at and do a "sujud sahwi" at the end before giving his own salam.