Welcome to the forum. Thanks for your question and for your kind wods about the forum.
You had entirely safe sex (congrats for a wise decision!) and can therefore be very confident that neither chlamydia, gonorrhea, nor any other traditional STD from those exposures is the cause of your upper respiratory infection and conjunctivitis. The vast majority of such infections result from garden-variety respiratory viruses. FYI, the most common true STD that causes conjunctivitis is chlamydia. Gonorrhea can do so, but rarely; and non-chlamydial NGU generally does not do so.
Having said that, it is conceivable you caught your URI and conjunctivitis from one of your commercial sex partners. Sex is obviously sufficiently close contact to transmit cold viruses, especially if there was any kissing. There's even one group of cold viruses (called adenovirus) that can infect the urethra, resulting in NGU in combination with conjunctivitis and/or other cold symptoms; below is a link to a forum question about it. However, with condom protection for oral sex, this isn't plausible in your case -- and you have had no symptoms to suggest urethritis.
http://www.medhelp.org/posts/STDs/Adenovirus-UTI/show/1780687
To your specific questions:
1) I agree exactly.
2) Your treatment sounds like a classical example of a doctor prescribing an antibiotic "just to be safe", knowing the problem is almost certainly viral. The large majority of upper respiratory infections, with or without sinusitid, are due to viruses -- and no virus responds to any antibiotic. In other words, I would not have prescribed azithromycin or any other antibiotic in this situation. But to answer your question directly, this AZM regimen, while not the recommended one for NGU, almost certainly would effectively treat it if you had it. There is no point in being evaluated for NGU. which cannot be diagnosed after treatment clears it up.
3) Alcohol does not significantly impair the effectiveness of any antibiotic, except if someone gets too intoxicated to remember to take the drug. But your AZM treatment wasn't necessary and won't have any effect on your URI anyway.
4) Yes. NGU -- whether due to chlamydia or other causes -- infects affected men's female sex partners. But it's not an issue here. You can safely continue sex with your partner, with no risk to her (except catching your cold).