Q1:
E. Culture of the discharge on modified Thayer-Martin media

Modified Thayer-Martin media is chocolate agar containing three antibiotics -- vancomycin, colistimethate, and nystatin -- to inhibit most Gram-positive, Gram-negative, and fungal normal flora, respectively. This media is sensitive and selective for culture of pathogenic Neisseria, which will appear as small, clear, oxidase-positive colonies after 24 hours of incubation. So, you will not get an immediate answer in this case.

Culture is difficult, because the organisms are quite fastidious; they will not survive very long in transport media or on a swab. Therefore, culture is most sensitive when it is done at the bedside (that is, directly from the patient to agar plate and immediately transported to the laboratory). Obtaining a culture is appropriate for diagnosis of gonorrhea in a few circumstances: 1) when there is concern for possible antimicrobial-resistant N. gonorrhoeae; 2) when public health authorities are conducting surveillance study; 3) in selected clinical cases when it is important to know the etiology, but simpler methods of diagnosis are negative. None of these circumstances applies in this case. So what else can you do? Try another option.