About 10-20% of men with nonchlamydial NGU have a relapse after threatment, so you are pretty typical. The usual approach (and the CDC recommendation) is to treat with the alternate recommended drug: doxycycline if originally treated with azithromycin (Zithromax) or the reverse if initially given doxy. There are no good data on whether it matters if men's female partners also are treated. Nonchlamydial NGU has never been proved to be harmful to women, so she likely is not at risk of a serious health outcome. However, it is unknown whether treating her might help prevent another recurrence of your symptoms.
1,2) It is uncertain whether your partner is at risk. See above.
3) There are no data on this, but I doubt your partner's IUD makes a difference.
4) I don't know what 'quick test' was done. Most likely it was a look under the microscope for gonorrhea, confirming your recurrent problem indeed was NGU and not gonorrhea.
At this point, I suggest you just see what happens in the next 1-2 weeks, and don't have sex during that time. Or if you just can't stand it, use condoms for either oral or vaginal. After a couple of weeks, resume unprotected sex. If the problem recurs yet again, then you and your partner both should be treated with doxycycline.
In the meantime, don't lose a lot of sleep over this. Nonchlamydial NGU has never been known to cause an important health outcome in men or women--no infertility, no urethral stricture, no cancer, etc--it's an inconvenience but probably not a serious health risk.
Good luck-- HHH, MD
Ive had persistent and reoccurring NGU for over a year now and most doctors are wrong about what a patient shold do while on the meds. The all say you can have protected sex which is wrong. I have been on meds and have had my symptoms almost completely gone but as soon as I had protected sex my symptoms came back in one or two days. Ive also heard that you can cosume alcohol while your body is fight of this superbug but I have donr that also and gotten the same results, after a night of drinking all symptoms returned and I was back on Dox yet again. IM still to this day tring to beat this thing but coincidently today my symptoms returned after a day of drinking and playing contact sports. I believe that the only way to beat this thing is to refrain from sex for at least a month and a half while on meds because a doc once told me that there are scars inside that need time to heal meaning no ejaculation or rough contact with the groing area