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.
Reciting the Quran with modulation is among the pious acts. The Prophet said: “Recite the Quran, for on the Day of Resurrection, it will come as an intercessor for those who recite it.” [Muslim]
Allah Says (what means): {…and recite the Quran (aloud) in a slow, (pleasant tone and) style.} [Quran 73: 4]
Indeed, the merit of Chapter Yaseen [Quran 36] is very great. However, to recite it every Thursday in a gathering in a given way after Maghrib is an innovation. Imam Ash-Shaatibi said when describing the definition of innovation: “It is an invented way in Islam similar to the legitimated acts. The purpose of following it is to exaggerate in worshipping Allah.”
Imam Ash-Shaatibi gave some examples for innovation; he said:
“Adhering to a certain method and manner is an innovation, such as making supplications in a gathering in one tone, or celebrating the birthday of the Prophet, or the like. And adhering to certain forms of worship in certain times without any evidence for doing so, such as fasting the fifteenth of Sha'baan and performing night prayers in that night.” [End of quote – Al-I’tisaam]
In the light of the above details, gathering every Thursday to recite Chapter Yaseen after Maghrib is an innovation. However, reciting it without fixing a certain day is permissible provided it is done according to the Sunnah.
As regards the second question, it is confirmed that Abu Hurayrah narrated that the Prophet used to recite in the Fajr prayer on Friday Chapter as-Sajdah [Quran 32] in the first Rak’ah, and in the second Rak’ah, he used to recite Chapter Al-Insaan [Quran 76] [Muslim]
Based on the above narration, it is a Sunnah to recite Chapter as-Sajdah in the Fajr Prayer on Friday, which contains a verse in which there is a prostration for the recitation of the Quran; this is the verse in which Allah Says (what means): {Only those believe in Our verses who, when they are reminded by them, fall down in prostration and exalt [Allah] with praise of their Lord, and they are not arrogant.} [Quran 32: 15]
However, it is better not to recite Surah as-Sajdah sometimes to prove that not reciting it sometimes is also permissible so that people would not believe that it is an obligation to recite it.
As regards celebrating the Prophet's birthday, it is an innovation.
For more benefit, please refer to Fataawa 81765, 81920 and 81804.
Allah knows best.