Welcome to the forum.
You clearly did not acquire HIV during the exposure described. The most important information in your detailed question is the negative test reslt at 37 days, which is around 99% reliable. Test results always overrule both symptoms and exposure history.
And in any case, both those factors also argue against HIV: this was a low risk exposure (because HIV is rare in women in the US, even among sex workers, and because of the brevity of penetration) and your symptoms are not at all suggestive of ARS or other manifestations of a new HIV infection. But even if you'd had an especially high risk exposure or typical symptoms, the test result is the evidence that counts.
To your specific questions:
1) No medicine have any effect on HIV antibody testing. Theoretically potent chemotherapy or immunosuppressive drugs might do it, but I stress theoretically: to my knowledge there are no reported cases in which it actually happened.
2) Around 99% conclusive; see above.
3) You really don't need further testing, but presuming you go ahead, the 6 week test will be sufficient. For sure it will be negative. It is no longer necessary to wait 3 months for conclusive antibody testing. See the thread linked below.
4) "They say ARS symptoms appear 4 - 6 weeks." Who they?? Nobody says that -- ARS symptoms typically start at 10-20 days. Generally ARS lasts 4-6 weeks. "I have been feeling excellent for the past two weeks, so could ARS start up again at 40 days post exposure." No way. I'm glad you're feeling well, but in any case your earlier symptoms were not at all suggestive of ARS anyway.
So all is well -- no worries. Thanks for your kind comment about our services. Here's that link:
http://www.medhelp.org/posts/show/1704700
Best wishes-- HHH, MD