How sound is the saying that "whoever accustomed himself to saying 'In the name of Allah, the Most Gracious, the Most Merciful' before every deed, will say it on the Day of Resurrection when he receives his record of deeds, and his sins will be erased, because Allah will treat him with the mercy by which he sought refuge"?

This statement is not a hadith. Such unseen matters should not be delved into with personal opinion; rather, they must be based on infallible revelation from the Quran or Sunnah. Accuracy is imperative when transmitting hadith, for the Prophet, peace and blessings be upon him, said: "Do not lie about me, for whoever lies about me shall enter the Fire," and "Whoever narrates a hadith from me which he deems to be a lie, then he is one of the two liars."