The most likely diagnosis for this patient with heavy menstrual bleeding, pelvic pain, hirsutism, acne, and elevated testosterone levels is polycystic ovarian syndrome (PCOS). PCOS is a common hormonal disorder in women of reproductive age, characterized by irregular menstrual cycles, hyperandrogenism (elevated androgen hormone levels leading to hirsutism and acne), and polycystic ovaries on ultrasound. Elevated serum testosterone levels and clinical features like hirsutism, acne, and irregular menses are all common manifestations of PCOS.

The most likely diagnosis for this patient with a thin, white, odorless vaginal discharge without itching or discomfort, who is sexually active with multiple partners, is Candidiasis (yeast infection). Candidiasis is characterized by a white, cottage cheese-like discharge and is typically odorless. It can occur in sexually active women, and the absence of itching or discomfort in this patient is not uncommon. However, laboratory testing may be required to confirm the diagnosis. It is important to consider sexually transmitted infections (STIs) as well, so testing for other STIs may also be indicated in this patient.

The most likely diagnosis for this patient with pelvic pain, dysmenorrhea, tender nodules on the posterior vaginal wall, and a fixed, retroverted uterus is endometriosis. Endometriosis is characterized by the presence of endometrial-like tissue outside the uterus, often causing pain and inflammation in the pelvic area. The initial treatment of choice is medical management with nonsteroidal anti-inflammatory drugs (NSAIDs), which can help relieve pain and inflammation. A definitive diagnosis and further management, such as laparoscopic surgery, may be considered if medical management is insufficient, but NSAIDs are an appropriate initial step in managing the symptoms associated with endometriosis. Other options a, c, and d do not align with the clinical presentation and findings in this scenario.