What is the correct saying between the two sayings for determining the time of Dhuhr, and does it begin when the eastern edge of the sun's disk crosses the meridian line, or when a person's shadow becomes equal to the length of his sandal strap, and is leaving the Dhuhr prayer in congregation because of that correct?

The Dhuhr time begins when the sun declines from the meridian, which is a matter of consensus. It is known by the start of the increase in the length of the shadow after it has reached its shortest point, or after it appears if it had no shadow at noon. So, when the shadow begins to increase after it has stopped decreasing, the Dhuhr time has begun.

The estimation of the sandal-strap (shirāk) in the Hadith of Gabriel (peace be upon him) differs; the sandal-strap is not for precise determination, but rather to indicate the minimum by which the sun's decline (zawāl) becomes evident. The shadow varies with time and place.

Dr. Sa'd Al-Khathlan objected to the resolution of the Fiqh Council that Dhuhr time coincides with the crossing of the center of the sun's disk over the meridian, asserting that it coincides with a prohibited time (waqt al-nahy), and that the correct view is that Dhuhr time begins with the crossing of the entire sun's disk. He added that some calendars add minutes to the time when the center of the sun reaches the meridian, indicating that the time added to achieve the legal zawāl is approximately three minutes.