Cardiac Output = Stroke Volume * Heart Rate
Increasing heart rate and/or stroke volume therefore increases cardiac output. The body does keep control of heart rate so to speak via parasympathetic nerves like the vagus nerve. However, when more blood is needed in tissues like during exercise, the heart rate must go up to increase cardiac output to deliver more blood. This means more deoxygenated blood is traveling through the veins to reach the pulmonary circulation. This increase in blood in the veins puts more pressure on the heart inducing an effect called "preload" that is essentially the heart accommodating a larger volume of blood. As a result the stroke volume increases to an extent as well. The contractility of the heart increases (This is called Frank Starlings Law) with a larger amount of volume. So, if the heart contracts more forcefully than before, blood pressure increases. However, the body adjusts for this by vasodilation in the peripheral circulatory system.
As for high blood pressure increasing cardiac output. Yes, I think this is true. But, it is not necessarily drastic. If one has an increased volume of blood the body will compensate by increasing the resistance through vasoconstriction (this results in high blood pressure). More resistance increases blood pressure. Higher blood pressure will increase preload and thus cardiac output. If anything is inaccurate or could be explained better, please chime in.