If a hypothyroid woman is on birth control pills alone(no levothyroxine), would it improve some of her symptoms like acne or hair loss?

Odd question: If she has low thyroid she will clearly benefit from thyroid therapy. Why not??? The specific type of birth control is significant. Some hormones reduce acne and improve hair problems. Some hormones (androgenic progesterones) aggravate acne and cause loss of scalp hair. All 3 of your meds reduce acne and reduce loss of scalp hair. For polycystic ovary, weight loss and perhaps metformin are useful.