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Bike-shedding captures the first part of the request (namely, "majoring on the minor" or "making mountains out of molehills") but doesn't appear to address the case of the underlying failing project. Bike-shedding can occur during while discussing either healthy or doomed projects.
IMHO, the phrase "Do you mind if..." is inelegant and imprecise. In many (if not most) cases, the asker doesn't really want to know the internal thoughts of the respondent; he or she simply wants to know if the respondent will allow it. The question demands mental gymnastics that can complicate the conversation: What if the respondent does mind, but will allow the action anyway? What if he or she doesn't mind, but knows of some reason that the asker isn't allowed to perform the action? I would prefer to hear the phrase "May I..." when the asker merely wants permission.
There isn't a correct yes/no answer. Consider the question "Have you stopped beating your wife?" No yes/no answer will be suitable because both questions are (I hope) based on incorrect premises, namely that you had open tickets and you are a wife beater.
As an American English speaker, I concur with your answer. Fever and temperature are interchangeable. "I think you have a temperature." is an acceptable way to communicate the message. "...have got..." also works, but isn't as pleasant.