Welcome to the forum. Thanks for your question.
My first thoughts and advice are to not worry much about NGU. When not caused by chlamydia, it is generally harmless both for infected men and their sex partners; and probably clears up on its own, probably over a few weeks. In other words, failing to diagnose NGU rarely has any important consequences. That said, I agree many (most?) practicing physicians don't understand NGU very well. (But one reason for that is the very fact of its usually non-serious nature. There's not a lot of scientific or social pressure to understand a trivial condition that's usually harmless.) This isn't to say it never causes harm, but that's definitely the exception, not the rule.
As for your discharge, it would be helpful to know more about it. How often? What time of day? Does anything trigger it, especaily a bowel movement or recent sexual arousal/erection? Also, say something about the sexual exposure(s) that made you seek STD testing in the first place.
To your specific questions:
1) The visual clarity of urethral fluid isn't the most important issue by a long shot. If there is no evidence of inflammation -- i.e. white blood cells in the urethra, or in the initial 1-2 tablespoons of voided urine -- then urethritis is absent. Your doctor's advice that abnormal discharge is "never" clear in appearance is an exaggeration, but it's not far off. Also, what patients report in clarity is often not confirmed by expert examination. In any case, absence of colored staining of white underwear is pretty good evidence there is no significant inflammation and therefore no NGU.
2) This is accurate on the initial 1-2 tbsp of urine. It has lesser value if you collected a midstream specimen. However, the best approach is to collect a swab specimen of the discharge, or even better the inside of the urethra, for microscopy.
3) Second opinion? Maybe, but from all you have said, my bet is that this also won't find anything abnormal. But you could see an infectious diseases or STD expert. Alternatively, perhaps make a new appointment with your docctor, take a printout of this thread, and use it as a framework for further discussion.
4) There is no lab test for NGU. The diagnosis is based on a combination of symptoms, examination (ideally when the patient hasn't urinated for several hours, e.g. first thing in the morning before first urination), and microscopy looking for urethral/urine WBC.
By far the most important facts here are that your STD lab tests were negative. I doubt you have NGU. In any case, I look forward to perhaps helping a bit more if you can answer the questions I asked above.
Best wishes-- HHH, MD