Here’s my answer to Question 1. Cognitive Dissonance is not directly detrimental to your health. It is a transitory state lasting only as long as your brain needs to reconcile the two conflicting concepts. As long as it doesn’t happen while you are driving or operating other heavy equipment, you will be fine. Our brains are amazing in their ability to adapt to changes, and cognitive dissonance is just an extreme form of this. Now, if the question was, “Is cognitive dissonance hazardous to your career?” then I would say, Absolutely! Thus the desire to avoid inducing cognitive dissonance in your stake holders.
Here’s my answer to question 2. As testers we often talk about multi-tasking and our ability to juggle planned testing with defect re-testing with exploratory testing and the myriad of other activities that we do. Recent research (see here and here for examples) seems to imply that multi-tasking is actually a myth. Testers require the same amount of dedicated time for each task that other people require. Where testers seem to have an advantage is our ability to incorporate unexpected information into our existing worldview. We are expecting the unexpected, so we adapt to change more easily. This is related to multi-tasking but not the same in my opinion. The best testers are able to pivot quickly to new tasks and more easily abandon concepts that are proven false. This also helps us be more resistant to cognitive dissonance, since our worldviews are necessarily more fluid to begin with.