Can I talk to my psychiatrist about suicidal thoughts without her telling anyone about them? I'm a teenager.

Depends. This is a difficult question to answer. The psychiatrist is, first and foremost, concerned about your safety. Just about everything you discuss with your psychiatrist is completely confidential. However, when it comes to things such as suicide, the psychiatrist will use their professional judgment to decide whether it is necessary to tell someone else.
No but keep reading. Your psychiatrist cannot promise not to tell because if you are at risk of hurting yourself he needs to protect you. Your psychiatrist would help you understand what is going on and help you protect yourself from doing anything that didn't make sense for you in the long run. Suicidal thoughts are different from actually harming yourself and you need the psychiatrists help in telling the difference.
I don't know. As I don't know your psychiatrist, I don't know what she'll do. If you were my patient and said you felt suicidal, I believe I would be ethically bound to do whatever was required to protect your safety.
Yes. Tell your psychiatrist about your thoughts and feelings. Please answer her questions honestly, she just wants to help you. You don't have to be in this alone. It's life saving to talk about your suicide ideation.
U conversion. With u psychiatrist is confidential, except if u r in danger of harming u self or others. Since we r obligated to interfer.