Keeping in mind that lying is stressful, what externally detectable signs might a lie detector identify, assuming it reliability

Lie detection or polygraph testing relies on Autonomic System arousal.  For polygraph lie detection, scientific validity rests on the strength of evidence supporting all the inferential links between deception and the test results. It is appropriate for making the discrimination between deception and truthfulness. Polygraph practice is built on comparing physiological responses to questions that are considered relevant to the investigation at hand, which evoke a lie from someone who is being deceptive. 

taking a bath requires the most water out of the given options because it takes a significant amount of water in order to fill a bathtub.

south, because if you took a map you would see texas is directly in the middle of east and west, but it is also downwards towards mexico, therefore it is south