What is the ruling on publishing specific adhkar (remembrances of God) and advising people to propagate them, and are the adhkar mentioned in the list authentic?

1. Ayat al-Kursi: Protection from Satan when sleeping, and entry into Paradise after death for whoever recites it after every obligatory prayer. 2. The last two verses of Surat al-Baqarah: Sufficient protection from harm or equivalent to performing Qiyam al-Layl (night prayer). The entirety of Surat al-Baqarah prevents Satan from entering the house for three days or nights. 3. Al-Ikhlas and al-Mu'awwidhat (Surat al-Falaq and Surat an-Nas): Sufficient protection from everything when recited three times in the morning and evening, recited after every prayer, and when sleeping, wipe the body with them. 4. "La hawla wa la quwwata illa billah" (There is no might nor power except with Allah): A treasure from the treasures of Paradise, and it is recommended to say it frequently. 5. "Bismillah illadhi la yadurru ma'a ismihi shay'un" (In the name of Allah, with whose name nothing can cause harm): Reciting it three times in the morning and evening protects from affliction. 6. "A'udhu bi kalimatillahit-tammati" (I seek refuge in the perfect words of Allah): Protects from evil and harm. 7. "Hasbiyallahu la ilaha illa Hu..." (Sufficient for me is Allah; there is no deity except Him...): Seven times is sufficient for worries. 8. "La ilaha illallahu wahdahu la sharika lahu..." (There is no deity except Allah, alone without partner...): A safeguard from Satan, and it has great virtues depending on the number of times it is said and its location. 9. "Bismillahi tawakkaltu 'alallah..." (In the name of Allah, I have relied upon Allah...): When leaving the house, it protects from Satan. 10. The supplication for entering the mosque: "A'udhu billahil-Azim..." (I seek refuge in Allah, the Most Great...): Protects from Satan throughout the day. 11. "Astaghfirullah alladhi la ilaha illa Huwal-Hayyul-Qayyumu wa atubu ilayh" (I seek forgiveness from Allah, other than whom there is no deity, the Ever-Living, the Sustainer, and I repent to Him): Forgives sins. 12. Sending prayers upon the Prophet: Suffices for worries and forgives sins. 13. Congregational prayer: No specific hadith regarding the mentioned virtue was found in the question, but its virtue is well-known. 14. Bidding farewell to a traveler: "Astawdi'ullaha dinaka wa amanataka wa khawatima 'amalik" (I entrust to Allah your religion, your trust, and the last of your deeds) for the one bidding farewell, and the traveler says: "Astawdi'ukumullah alladhi la tadi'u wada'i'uhu" (I entrust you to Allah, with whom nothing is lost). 15. Supplications for repelling Satan: Refer to fatwa no. 35456. 16. Basmalah (Saying "Bismillah"): Recommended at the start of every action. 17. Supplication for distress: "La ilaha illallahul-'Azimul-Halim..." (There is no deity except Allah, the Most Great, the Most Forbearing...). 18. Saying "Assalamu 'alaykum" to Allah: This is incorrect; the correct phrasing is "At-Tahiyyatu lillah" (All greetings are for Allah). 19. Supplication of the disobedient servant: Refer to fatwa no. 74618. 20. "Subhanaka ya Allah ya Rahim ya Ghafur ya Wadud" (Glory be to You, O Allah, O Most Merciful, O Most Forgiving, O Most Loving): Good words, but not authentically established from the Prophet, peace be upon him.

Conclusion: One should adhere to the adhkar (remembrances) and supplications authentically established in the Sunnah. It is permissible to spread good adhkar while being careful not to attribute them to the Prophet, peace be upon him, unless their authenticity is confirmed.