T.,
I am nowhere near your situation as my daughter is only 4, but I DO know that our blessed little angels are a challenge at all ages.
First of all, I am glad you took the door off. I would remove the curtain too. When she complains that you have taken her privacy, simply say, "You will need to earn your privacy back. I love you and I am here for you when you are ready to be honest and respectful. There are no secrets in my home."
Tough love! I have even removed my 4 year olds door because she woud slam it when she was angry. It was off for a week - and she doesn't slam the door anymore! I think it was Vanessa Williams on Oprah that said she went all through high school with no door on her bedroom because of her behavior. It was a mother's day episode and she was on with her mom. Her mom responded by saying, " I am her mother, not her friend. And I don't need to be her friend, she needs a mother. She has plenty of other friends." something to that effect...
Second, make her get a job. 16 is old enough to have one and she will need money to buy her own school clothes, shoes, etc, if she continues the behavior (catch my drift?) - don't provide her with the luxaries that she is used to getting if she is not behaving in a way that warrants having them. Further, take away any materialistic posessions that she can't live without if she keeps it up. Working for a living never hurt anyone!
Lastly, I would tag along with her everywhere she goes. I know it is impossible to keep her home or be home at all times with her, but if you have friends who are understanding, plan your girltime in a location your daughter is. At 16, I am sure she will be annoyed seeing you everywhere she is, but it goes back to earning your respect and trust. You don't need to earn hers!
Counseling probably wouldn't hurt either, if you can get her to go; just remember that these are all things done out of love and concern to keep her on the right path.
And to the mom who responded about your priorites, it was very harsh! Some compassion for another mom would be better received. It's pretty clear that you posted because you are concerned for your daughter and not your puppy!
Best of luck to you all,
G.