I'll pick the second option: "On average, is there a difference in people’s blood pressure before and after giving a speech?"
In this case, the independent variable is whether the blood pressure measurement is taken "before" or "after" giving a speech. This is an experimental condition that is being manipulated.
The dependent variable is the blood pressure measurement itself, as it is the outcome being measured to see if there is any effect due to the independent variable (the timing of the measurement).
This situation represents a paired sample comparison (dependent samples) because the same individuals' blood pressure is measured at two different times (before and after the speech).