When the slope of a line is 0, does that mean the slope is undefined.

Think about what slope means. Slope is a number that indicates whether a line is increasing in length (slope>0) or decreasing (slope<0). If your slope is 0, it signifies that your line is absolutely level and neither ascends nor descends (is neither positive nor negative). So answer is no, the definition of it is slope=0, which indicates that your line is absolutely level.