Do any other androgens other than DHT contribute to MPB? And is there a difference between like injecting testosterone like steroids and rises in natural body testosterone from i.e. going to the gym, eating meat, etc.?
Androgens cause balding. For example, women who have polycystic ovary syndrome / PCOS (who produce androgens) get into the male balding process, plus the appearance of facial hair (though not as much as we men). I think that if you look at the biochemical metabolic pathways, you will see many similarities of testosterone and DHT to other androgens. I do not believe that working out or eating meat will cause you to raise you testosterone (long term) to a point that causes you to lose hair.
For a list of androgens see Wikipedia.
I would trust your doctor to treat your thyroid issues with the dose of medication that he prescribed, but Synthroid (levothyroxine) does list “mild hair loss” as a possible side effect (see 
Coumadin (warfarin) is an anticoagulant, also known as a blood thinner. Blood thinners are on the top of the list of medications which must be addressed in a patient who is about to have a hair transplant. I have done transplants on people who are on such medications, but take many steps in the process to assure safety. Generally, one can cut back on the Coumadin and then step it up on the day of transplants. Your general health is really the issue and the reason you are on these medications may allow you to stop them for a week or so. The answer therefore is an individualized answer depending upon the patient, his/her medical condition causing the use of such a medication, and the general state of the patient’s health.