Before answering the three questions, I want to clarify that the vignette provided would suggest this individual is experiencing an ascending aortic dissection rather than a descending. The reasoning behind this is if a patient loses their radial pulses bilaterally, it would indicate that damage has occurred in the aorta before the brachiocephalic trunk (first trunk off the aorta that supplies the right arm). Furthermore, high blood pressure (hypertension) is more classically associated with ascending aortic dissection (type A) due to the high pulsatile pressure being placed on the aorta from the left ventricle. In contrast, descending aortic dissections (type B) are more classically associated with atherosclerosis.
A. An aortic dissection is the creation of a false lumen, or space, between the layers of the aorta, specifically the intimal and medial layers. Therefore, any disruption to the intima that creates a defect will allow the high-pressure, pulsatile blood being pumped out of the left ventricle to enter this space and further expand it. As for why poorly controlled high blood pressure (hypertension) is an etiological factor, this goes back to the intima. Hypertension results in high pulsatile pressure and increased shearing forces acting on the wall of the aorta. Over time, this will result in thickening of the intima, weakening of the media and overall increase the stiffness of the aortic vessel. Eventually, these high pressures and shearing forces will create a tear in the intima and blood will flow into the false lumen due to the decreased resistance to flow (fluids will take the path of least resistance).
B. As I mentioned in the first paragraph, the aorta has three main branches that come off the aortic arch, in order being brachiocephalic (right arm and right carotid artery), left common carotid, and left subclavian. Blood pressure and radial pulses in the right arm are supplied by blood flowing through the brachiocephalic trunk whereas the left subclavian supplies the left arm. Therefore, in order for this individual to suddenly lose blood pressure and radial pulses in both arms, he would need to have a defect proximal (before) these branches; specifically, before the brachiocephalic trunk. The reason his pressures and pulse became unobtainable is that instead of the blood and associated pressure being moved through the main lumen of the aorta, the blood and subsequent pressures are being diverted into the false lumen created by the dissection as there is less resistance here. Because this false lumen has been created before the brachiocephalic trunk, less blood (and therefore pressure) will reach the right arm and subsequently the left arm via the left subclavian artery.
C. The reasoning for aggressive blood pressure control and pulsatile blood flow is to minimize the damage being done to the aorta; specifically, you are reducing aortic wall tension and subsequent extension of the dissection. In the case of an acute ascending aortic dissection, surgical management is a must as this is a surgical emergency.