What is the authenticity of the hadith: "Space will be made for the stranger in his grave according to his distance from his family," and does it have an origin? And what is the authenticity of the hadith: "There is no deceased person who dies in a foreign land except that the space between his grave and the end of his trace in Paradise will be measured for him," or similar wording?

The first hadith ("He will be given ample space in his grave, as far as his distance from his family") has no found chain of transmission.

As for the second hadith ("Indeed, when a man dies in a place other than his birthplace, his space from his birthplace to the end of his trace in Paradise will be measured for him"), scholars have differed regarding its authenticity due to disagreement about one of its narrators and its apparent contradiction with the encouragement to die in Medina. Some scholars have reconciled this hadith with the hadiths extolling the virtues of dying in Medina by interpreting it as referring to someone who died in Medina while being a stranger to it, thus receiving a virtue greater than one who was born and died there.

As for the other hadiths that indicate that whoever dies as a stranger dies as a martyr, all of them are weak and not authentic.