What happens during bypass surgery? do they cut the sternum or rib cartilages?

Depends: Usually sternum is split longitudinally. For limited procedures, a couple of ribs can be cut to create a flap or window. Depends on the preference of the surgeon and the extent of the access required.

Sternum: Most cases require the sternum to be divided.

Sternum commonly: In most the skin, soft tissue, sternum, pericardium are divided!. This shows the heart so the coronary arteries can be seen and bypassed.