It is mustahabb to stay in the mosque after Fajr prayer until the sun rises, because this is what the Prophet (peace and blessings of Allaah be upon him) and his companions did, and because there is great reward in that. Muslim (670) narrated from Jaabir ibn Samurah that when the Prophet (peace and blessings of Allaah be upon him) had prayed Fajr, he would sit in his prayer place until the sun had risen properly.
And Muslim also narrated (670) that Sammaak ibn Harb said: I said to Jaabir ibn Samurah: Did you sit with the Messenger of Allaah (peace and blessings of Allaah be upon him)? He said: Yes, frequently. He would not get up from the place in which he had prayed Fajr until the sun had risen, and when the sun had risen he would get up. They used to chat and talk about matters of the Jaahiliyah, and they would laugh but he smiled.
Al-Tirmidhi narrated that Anas ibn Maalik (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “Whoever prays Fajr in congregation then sits remembering Allaah until the sun rises, then prays two rak’ahs, will have a reward like that of Hajj and ‘Umrah.” He said: The Messenger of Allaah (peace and blessings of Allaah be upon him) said: “In full, in full, in full.”
This hadeeth was classed as hasan by al-Albaani in Saheeh al-Tirmidhi.
This points to the virtue of sitting in the mosque after Fajr prayer, and the virtue of praying two rak’ahs when the sun has risen fully.
In general, if a person stays in the mosque to remember Allaah (dhikr) and worship Him, or waiting for the prayer, all of these are good deeds and acts of worship that bring one closer to Allaah. Al-Bukhaari (445) and Muslim (649) narrated from Abu Hurayrah that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “The angels send blessings upon one of you so long as he is in his prayer-place where he offered his prayer, so long as he does not break his wudoo’; they say: ‘O Allaah forgive him, O Allaah have mercy on him.’”
Based on this, your brothers have done well by staying in the mosque to remember Allaah, and we ask Allaah to reward them.
Reading Qur’aan together in unison is not prescribed, because it is not mentioned in the Sunnah. And if it is done in a loud voice that disturbs those who are remembering Allaah and sitting there, then it is even more disliked, because of the general meaning of the words of the Prophet (peace and blessings of Allaah be upon him): “When one of you stands in prayer, he is conversing with his Lord, so let one of you know what he is saying to his Lord and do not raise your voices above one another in reciting when praying.” Narrated by Ahmad (4928) and classed as saheeh by Shu’ayb al-Arna’oot in Tahqeeq al-Musnad.
It says in Fataawa al-Lajnah al-Daa’imah (4/112): What is the ruling on reciting Qur’aan together in the mosque?
Answer: The question is somewhat vague. If what is meant is that they recite together in unison, pausing and stopping at the same time, this is not prescribed, and at the very least it is makrooh, because there is no report from the Prophet (peace and blessings of Allaah be upon him) or from the Sahaabah that they did that. But if that is done for the purpose of teaching, then we hope that there is nothing wrong with it. But if what is meant is that they gather to read Qur’aan in order to memorize it or learn it, and one of them reads whilst the others listen, or each of them reads to himself without raising his voice or reading in unison with others, then that is prescribed, because it is proven that the Messenger of Allaah (peace and blessings of Allaah be upon him) said: “No people gather in one of the houses of Allaah, reciting the Book of Allaah and studying it together, but sakeenah (tranquillity) descends upon them and the angels surround them and mercy covers them, and Allaah remembers them to those who are with Him.” Narrated by Muslim. End quote.
It also says (4/39):
Question: Is it permissible to recite Soorat Yaa-Seen out loud in the mosque or not? Answer: It is not permissible for anyone to raise his voice when reciting Qur’aan in the mosque, whether it is Soorat Yaa-Seen or any other soorah of the Qur’aan, whether in prayer or otherwise, because it is proven that the Prophet (peace and blessings of Allaah be upon him) came out to the people when they were praying and reciting Qur’aan out loud, and he said: “O people, each of you is conversing with his Lord, so do not raise your voices above one another in reciting.” And because by doing that they distract and disturb one another. End quote.
These readers should be advised and called in a gentle manner.
And Allaah knows best.