Can people under 18 have plastic surgery and cosmetic surgery without their parents consent?

No. No, any patient under the age of 18 must have a parent or legal guardian sign the consent form for surgery. Beware of any person willing to perform procedures on a person under 18 without parental consent.
No, for good reason! Physical development is rarely complete before age 18. More importantly, this is a major decision affecting you and your body. Not involving your parents sets up a tense situation. Open and honest discussion is always best. Consider this, if you can't be persuasive enough in your argument for surgery, maybe best to wait until you have the maturity to better make your case!
Cosmetic surgery. Not unless they are legally emancipated.
No. No, unless the patient is an emancipated minor he/she must have parental or guardian consent to proceed with surgery under the age of 18.
Best not to. Usually, a patient under age requires his parent or guardian to consent to the procedure. But more importantly, it is always best to attend a consultation with an adult who is looking out for your best interests. Having another set of ears to listen to the benefits and potential risks will be invaluable. Actually, anyone planning a cosmetic procedure will benefit from another to be there..
Sometimes. If you are under 18 and you live and support yourself, you are considered an emancipated minor, and can legally receive surgery. Having said that, do yourself a favor, and wait until all physical development is complete prior to cosmetic surgery. Congenital correction and reconstructive surgery are fine, but cosmetic surgery should be time and age appropriate.
Consent. No procedure can be performed on anyone under the age of 18 without their parents or guardians consent.
No. Patients under the age of 18 need the permission of their parents. Physicians may proceed in some rare, emergent cases to save life, limb, or severe disfigurement.