Is it considered a violation of Islamic law to leave a one-meter space to the north of the row in the mosque to protect worshippers, and to draw a line on the ground to clarify this, such that the row is not completed?

The fundamental principle regarding prayer rows is that they should be complete. One should not start the second row if there is an empty space in the first. The evidence for this is the hadith narrated by Jabir ibn Samurah in Sahih Muslim: "Will you not arrange yourselves in rows as the angels arrange themselves in rows before their Lord?" We asked, "How do the angels arrange themselves in rows?" He replied, "They complete the first rows and stand close together in the row."

It has become customary in some mosques to leave a passageway at the end of the row—either to the right or left—from the first row to the back of the mosque. This is for passage, entry, and exit. They place a demarcation line to indicate the end of the row and that what follows is a passageway. This allows someone whose ablution might break to exit, or someone who wishes to leave immediately after the Imam's salutations to do so without stepping over rows or passing in front of someone who is still praying (making up missed prayers) or performing supererogatory prayers.

If this is what the questioner is asking about, then we hope there is no harm in creating such a passageway. In this case, the end of the row would be at the demarcation line between the row and the passageway.