The external iliac artery is a branch of the common iliac artery. It becomes the femoral artery as it passes thru the inguinal canal. The abdominal aorta gives rise to the common illiac artery, but not the femoral artery directly. The brachiocephalic trunk supplies the head and neck and gives rise to the right common carotid artery and right subclavian artery. The internal iliac artery gives rise to a series of branches that supply the medial thigh, the buttock and pelvic area.

The tongue is innervated by a many cranial nerves. Taste from the anterior two-thirds of the tongue is transmitted by the facial nerve (VII), and from the posterior one-third of the tongue, by the glossopharyngeal nerve (IX). Sensation of the anterior two-thirds of the tongue is transmitted by the trigeminal nerve (V) and from the posterior one third by the glossopharyngeal nerve. The motor innervation of the tongue is thru the hypoglossal nerve (XII).

The aorta traverses the diaphragm at level T12. Other structures that traverse the diaphragm are the esophagus, the vagus nerve, the azygos vein, the thoracic duct and the inferior vena cava. The axillary, femoral, pulmonary and common carotid arteries are branches of the aorta, but they do not cross the diaphragm.

The nerve most likely injured in this patient is the left recurrent laryngeal nerve. The left recurrent laryngeal nerve, which is a branch of the vagus nerve (cranial nerve X), and is responsible for innervating the muscles of the larynx that contribute to moving the vocal folds. Therefore, if there is an injury to the left recurrent laryngeal nerve, the laryngeal muscles will be affected, weakening movement of the vocal folds, and causing a hoarse voice and difficulty swallowing, as is present in this patient. 

The facial nerve is responsible for a number of functions including facial movements and taste, but not voice or swallowing.

The long thoracic nerve innervates the serratus anterior muscle. When injured, this can result in a "winged scapula," but not voice or swallowing changes. 

The trigeminal nerve is responsible for a number of functions including chewing, biting, and facial sensation, but not voice or swallowing.

There is no such nerve as the "esophageal nerve."

The cavernous sinus is unique in which it uses the superior petrosal sinus to drain into the transverse sagittal sinus. Whereas, the straight, superior sagittal sinus, and cerebellar sinus all drain into the confluence of sinuses. Then the confluence of sinuses later drains into the transverse sagittal sinus as well.

The right pulmonary vein supplies blood to the left atrium.

The internal iliac artery is responsible for a number of branches including:the iliolumbar, lateral sacral, superior gluteal, obturator, inferior gluteal, umbilical, uterine, vaginal, inferior vesical, middle rectal, and internal pudendal arteries. 

The duodenum receives arterial blood from two sources, the celiac trunk and the superior mesenteric artery.  The proximal duodenum is supplied by the gastroduodenal artery and its branch the superior pancreaticoduodenal artery. Both of these branches are supplied by the celiac trunk. The distal duodenum (midgut) is supplied by the superior mesenteric artery and its branch, the inferior pancreaticoduodenal artery. Although the superior and inferior pancreaticoduodenal arteries have different sources they form an anastomatic loop between the celiac trunk and superior mesenteric artery.

The superior mesenteric artery arises off the anterior surface of the abdominal artery just inferior to the celiac trunk (around L1). The superior mesenteric artery (and its branches) supplies the intestine from the distal duodenum to the proximal two thirds of the transverse colon. It also supplies the pancreas.

The intercostal space is the space between two ribs. As there are 12 ribs on each side, there are 11 intercostal spaces which are numbered for the rib superior to it. Within the intercostal space there are muscles, lymph nodes, nerves, arteries and veins. The vein, artery, and nerve (in this order) run together in the neurovascular bundle within the intercostal space. The neurovascular bundle runs directly inferior to the rib.