Is there any evidence to say that I should recite Al-Faatihah quietly in the prayers in which the Quran recitation is done aloud, whether I join the imam late or on time? Also, if I catch one unit of the Maghrib prayer, should I recite the Quran aloud for the next unit, praying on my own to complete my prayer? And I have the same question for when I catch one unit of the Fajr prayer; do I recite the Quran out loud for the next one?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger. 

As for the person who is being led in the prayer that is recited loudly – whether he reached the prayer from the start or was late – according to the view of the majority of the scholars, it is sufficient for him to listen to the recitation of the imaam, and he does not have to recite Al-Faatihah or any other soorah. However, some scholars are of the view that he is obliged to recite Al-Faatihah. This is better in order to be on the safe side and avoid the difference of opinion.

Ibn Qudaamah said:

“In brief, if the person who is led in prayer can hear the recitation of the imaam, then he is not obliged to recite Al-Faatihah. The recitation of Al-Faatihah is not even recommended according to our Imaam (Ahmad ibn Hanbal), Maalik, Is-haaq, and the scholars of the Hanafi School; this is also one of the two views of Ash-Shaafi'i and a group of the Salaf (the righteous predecessors). The other view of Ash-Shaafi'i is that he recites what the imaam recites loudly, because of the general saying of the Prophet ‘The prayer is invalid for the one who does not recite the opening Chapter of the Quran (i.e. Al-Faatihah).’” [Al-Bukhaari and Muslim] 

‘Ubaadah ibn As-Saamit, may Allah be pleased with him, narrated, “We were behind the Prophet in the Fajr prayer, and he recited (the Quran), but the recitation became difficult for him. Then, when he finished, he said, ‘Perhaps you recite behind your imaam?’ We replied, ‘Yes, it is so, O Messenger of Allah.’ He said, ‘Do not do so, except for Al-Faatihah, for the one who does not recite it, his prayer is invalid.’” [Al-Athram and Abu Daawood] 

Allah says (what means): {So when the Quran is recited, then listen to it and pay attention that you may receive mercy.} [Quran 7:204] 

Moreover, Imaam Ahmad said about the hadeeth which was reported by Abu Daawood, “The Muslims agreed that this verse applies to prayer. Because it is general, so it includes the prayer with its generality.” Also, Abu Hurayrah, may Allah be pleased with him, narrated that the Prophet said, “The imaam is appointed so that he would be followed; so if he says ‘Allahu Akbar’, then say ‘Allahu Akbar’; if he recites, then listen attentively to him.” [Muslim]" [Abridged]

If a person who is led in prayer misses the first Rak‘ah (unit of prayer) of the Maghrib, then after the imaam concludes the prayer by saying the Salaam, he should make up one Rak‘ah by reciting Al-Faatihah only and silently, then sit for the Tashahhud, and then say the Salaam (concludes the prayer). This is the view that we adopt here in Islamweb; that is when a person joins the congregation with the imaam, which is considered the first Rak‘ah of his prayer.

Ibn Baaz was asked:

“A man entered the mosque to pray the Maghrib and caught two Rak‘ahs with the imaam and prayed the last Rak‘ah alone. Should he recite Soorah Al-Faatihah aloud in this Rak‘ah on the basis that he prayed the last Rak‘ah with the imaam?

Answer: The Rak‘ah that he made up after his Imaam concluded the prayer with Salaam is considered his third Rak‘ah, so it is not permissible for him to recite aloud in it, because the correct view of the two scholarly opinions in this regard is that what a person who is preceded in the prayer caught with the imaam is considered the beginning of his prayer, and that what he makes up [after the imaam concludes the prayer] is considered the ending of his prayer, as the Prophet said, ‘When you come to pray, do not come rushing, but come walking in a dignified manner, and whatever you catch up with, you pray, and whatever you have missed, complete it.’” [Al-Bukhaari and Muslim]

As for the one who missed the first Rak‘ah of the Fajr prayer, then he must make up for it aloud, but he should not recite in a way that disturbs the worshipers.

The fatwa of the Standing Committee for Issuing Fataawa reads:

"Question: If I miss a Rak‘ah of the Fajr prayer, is it permissible for me to recite aloud in the last Rak‘ah?

Answer: You recite Al-Faatihah and whatever part of the Quran aloud, but you should not disturb the worshipers around you when making up for the Rak‘ah that you failed to pray with the imaam.”

Allah knows best.