What are the functions of different parts of the kidney (Aorta, renal vein, renal artery, vena cava etc) ? . . .
None of these are parts of kidney, these are all blood vessels.
Aorta is the largest artery present in the body. It originates from the left ventricle and extends down to the abdomen. Aorta is the first blood vessel through which oxygenated blood from heart starts its journey to all parts of the body except lungs.
Renal veins are the blood vessels which return blood from the kidneys to the vena cava which then drains the blood into heart.
Renal artery brings oxygenated blood to the kidneys from the aorta.
Vena cava is the vein that brings deoxygenated blood from the body to the heart. There are anterior and posterior vena cava, anterior vena cava brings the deoxygenated blood from the upper part of the body while posterior vena cava brings deoxygenated blood from the lower part of the body.