Is this a sound hadith from Ali (may Allah be pleased with him): "Whoever recites Surat al-Ikhlas a thousand times on the Day of Ashura, the Most Merciful will look upon him, and whoever the Most Merciful looks upon, He will never punish him"? And are there any specific adhkar for the Day of Ashura that have a particular virtue?

The hadith, "Whoever recites Surat al-Ikhlas a thousand times on the Day of Ashura..." is unsound and has no basis. It is a report circulated in Shiite books without an isnad (chain of narration). Sheikh Al-Albani said: "I do not know of any sound hadith regarding the virtue of reciting 'Qul Huwa Allahu Ahad' a thousand times; rather, everything narrated concerning it is very weak." The established virtuous act on the Day of Ashura is fasting, as Ibn Abbas (may Allah be pleased with them both) said: "I never saw the Prophet (peace and blessings of Allah be upon him) so keen to fast any day, giving it preference over others, except this day, the Day of Ashura, and this month—meaning the month of Ramadan." Ibn al-Qayyim said: "The hadiths about applying kohl on the Day of Ashura, beautifying oneself, being generous, and performing prayers on it, and other such virtues: none of them are sound, not a single hadith. Nothing has been authentically reported from the Prophet (peace and blessings of Allah be upon him) concerning it except the hadiths about fasting it; everything else is false."