On the posterior abdominal wall:  the lumbar vessels run anterior to psoas major  the kidneys are retroperitoneal viscera and lie on psoas major  peritoneal reflections pass as mesenteries to surround intraperitoneal viscera  the thoracolumbar fascia gives origin to rectus abdominus muscle  quadratus lumborum lies medial to psoas major

The lumbar vessels run anterior to psoas major: This statement is correct. The lumbar vessels, which include the lumbar arteries and veins, are located anterior to the psoas major muscle. They supply blood to the muscles and skin in the lower back region.

The kidneys are retroperitoneal viscera and lie on psoas major: This statement is also correct. The kidneys are indeed retroperitoneal organs, meaning they are located behind the peritoneum, the lining of the abdominal cavity. They are positioned on either side of the vertebral column and lie on the psoas major muscle.

Peritoneal reflections pass as mesenteries to surround intraperitoneal viscera: This statement is correct. The peritoneum is a continuous membrane that lines the abdominal cavity and covers the abdominal organs. The mesenteries are double layers of peritoneum that extend from the body wall to the organs, providing a pathway for blood vessels, nerves, and lymphatics. They surround the intraperitoneal organs, which are completely encased by peritoneum.

The thoracolumbar fascia gives origin to rectus abdominus muscle: This statement is incorrect. The rectus abdominis muscle originates from the pubic symphysis and pubic crest, not the thoracolumbar fascia. The thoracolumbar fascia is a deep investing membrane which covers the deep muscles of the back of the trunk.

Quadratus lumborum lies medial to psoas major: This statement is incorrect. The quadratus lumborum muscle is actually located lateral to the psoas major muscle, not medial. It is a muscle of the posterior abdominal wall, lying deep to the psoas major muscle.