With regard to evidence for events and places and customs described in Genesis, I found two articles that shed light on the journey of Abram and his family clan, Terah. Thousands of tablets have been found in the ruined palace at Mari confirming the places and peoples mentioned in the Genesis account. Below are brief extracts from the two articles, along with the links so you can read them in their entirety:
The saga of Abraham unfolds between two landmarks, the exodus from “Ur of the Chaldeans” (Ur Kasdim) of the family, or clan, of Terah and “the purchase of” (or “the burials in”) the cave of Machpelah. Tradition seems particularly firm on this point. The Hebrew text, in fact, locates the departure specifically at Ur Kasdim, the Kasdim being none other than the Kaldu of the cuneiform texts at Mari. It is manifestly a migration of which one tribe is the centre. The leader of the movement is designated by name: Terah, who “takes them out” from Ur, Abram his son, Lot the son of Haran, another son of Terah, and their wives, the best known being Sarai, the wife of Abram. The existence of another son of Terah, Nahor, who appears later, is noted.
Most scholars agree that Ur Kasdim was the Sumerian city of Ur, today Tall al-Muqayyar (or Mughair), about 200 miles (300 km) southeast of Baghdad in lower Mesopotamia, which was excavated from 1922 to 1934. It is certain that the cradle of the ancestors was the seat of a vigorous polytheism whose memory had not been lost and whose uncontested master in Ur was Nanna (or Sin), the Sumero-Akkadian moon god. “They served other gods,” Joshua, Moses’ successor, recalled, speaking to their descendants at Shechem.
Abraham had not yet come to the end of his journey. Between Shechem and Bethel he had gone about 31 miles (50 km). It was about as far again from Bethel to Hebron, or more precisely to the oaks of Mamre, “which are at Hebron” (according to the Genesis account). The location of Mamre has been the subject of some indecision. At the present time, there is general agreement in setting it 1.5 miles (3 km) northwest of Hebron at Rāmat al-Khalīl, an Arabic name which means the “Heights of the Friend,” the friend (of God) being Abraham.
Another article discusses new light on the era of city-states which corresponds more closely to Abraham's time. Among these artifacts are some 20,000 clay tablets found deep inside in the ruins of the city of Mari in today's Syria. 2,000 clay tablets were found in the ruins of Mari, which was located on the Euphrates River some 30 miles north of the border between Syria and Iraq. In its time, Mari was a key centre on the trade routes between Babylon, Egypt and Persia (today's Iran).
Mari was the capital of King Zimri-Lim in the 18th century B.C. until it was conquered and destroyed by King Hammurabi. In the late 20th century A.D., French archaeologists looking for Mari dug through centuries of sand to uncover Zimri-Lim's former palace. Deep within the ruins, they discovered tablets written in an ancient cuneiform script, one of the first forms of writing. Some of the tablets have been dated back 200 years before Zimri-Lim's time, which would place them around the same time that the Bible says Abraham's family departed Ur. Information translated from the Mari tablets would seem to indicate that the Sumerian Ur, not Ur of the Chaldeans, is more likely the place where Abraham and his family started their journey.
The Biblical World notes that some of the Mari tablets use words from the Amorite tribes that are also found in Abraham's story, such as his father's name, Terah, and his brothers' names, Nahor and Haran (also ironically the name for their destination). From these artifacts and others, some scholars have concluded that Abraham's family may have been Amorites, a Semitic tribe that began to migrate out of Mesopotamia around 2100 B.C. The Amorites' migration destabilized Ur, which scholars estimate collapsed around 1900 B.C.
Although there may be differences of opinion with regard to some dates or the location of some places, there can be no doubt as to the reality of the events, places and customs described in the Genesis account of Abraham.