To what extent is it lawful to regularly hold a daily Quranic study circle (halaqa) after Fajr prayer, where each individual recites a portion of the Quran, concluding with a collective supplication, and is it true that this was not transmitted from the Salaf?

It is permissible to regularly attend a circle for reading the Quran in the mosque or elsewhere, provided that no specific virtue is believed for it at a particular time. It is also permissible to listen to a single reciter while others are seated. Each individual reading the Quran by themselves is better than collective reading in one voice (Qira'at al-Idarah), which some scholars disliked, but Qira'at al-Idarah is considered good by most scholars. It is recommended to supplicate after reciting the Quran, and supplication after finishing a lesson of knowledge is permissible. However, collective supplication in one voice and in unison is an innovation (bid'ah).