How does hypertension increase cardiac output?

It doesn't. Hypertension increases a parameter known as after load (the obstacle the heart is working against). All other things being equal, high blood pressure produces less volume of blood pumped with each heartbeat for any given amount of work by the heart. The heart thus increases how hard it is working with each beat which is one of the ways in which heart damage results from hypertension.
It doesn't. In a physiologic model, increased blood pressure or "hypertension" or increased "afterload" tends to decrease cardiac output. In a complete animal or human model, there are various reflexes that work to maintain cardiac output in the face of increased afterload but they shouldn't cause an increase in cardiac output relative to the baseline.