What is the authenticity of the mentioned Hadith: "Whoever prays four [rak'ahs] and supplicates before Al-Hajirah, it is as if he prayed them on Laylat al-Qadr, and when two Muslims shake hands, no sin remains except that it falls away"? And what is meant by Al-Hajirah and the four rak'ahs?

This narration is weak. It was narrated by Al-Bari in "Al-Tareekh Al-Kabeer" and Al-Bayhaqi in "Shu'ab Al-Iman" and others, from Al-Bara bin Azib, مرفوعاً (Marfu'an) [attributed to the Prophet]: "Whoever prays four rak'ahs before Al-Hajirah, it is as if he prayed them on Laylat Al-Qadr. And if two Muslims shake hands, no sin remains between them but it falls away."

In its chain of narration is Mansour bin Abdullah, whose status is unknown, and no authentication has been reported for him except Ibn Hibban's mention of him in "Al-Thiqat" (The Trustworthy). And his shaykh, Sahl bin Tammam bin Bazi', makes mistakes and is prone to error.

Al-Hajirah is the time of intense heat at midday. Some commentators have interpreted it as the Duha prayer, and others as the Sunnah prayer of Dhuhr. There are authentic hadiths that suffice and render this weak narration unnecessary regarding the virtue of Duha prayer and the regular Sunnah prayer of Dhuhr.