Is playing religious songs with music that mention God and His Messenger—may God’s prayers and peace be upon him—considered an insult to their names, especially when accompanied by joking speech about intercourse? And is supplicating and seeking forgiveness after such a gathering considered mockery of supplication?

None of the actions mentioned are considered nullifiers of Islam. One must be cautious of obsessive thoughts (waswas) and yielding to Satan in these ideas.

It is recommended to occupy oneself with learning, da'wah (inviting to Islam), serving family and community, associating with the righteous, and avoiding gatherings with those devoted to musical instruments and songs.

The Sharia has forbidden all types of music, and the proof for this is the Hadith in Bukhari: "There will be among my Ummah people who will consider lawful adultery, silk, intoxicants, and musical instruments (ma'azif)," and the Hadith in Abu Dawud, Ahmad, and Al-Bayhaqi: "Indeed, Allah has forbidden to me – or forbidden – Khamr (intoxicants), gambling, the kubah (drum), and every intoxicant is haram."

Dhikr (remembrance of Allah) accompanied by songs with musical instruments is prohibited.

Kufr (disbelief) does not occur through these actions unless there is an intention to mock Allah or His Messenger (peace be upon him).

Merely making supplication after finishing a feast is neither mockery nor is there any harm in it.