No. This is a medical procedure. You will need parental permission, unless you are an emancipated minor.
Liposuction. Legally speaking, yes. But whether its a good idea or not, I can not comment on. That is between you, your parents and your surgeon. Remember it is surgery with potential risks and complications.
No. Cosmetic procedures at that young of an age have ethical considerations that must be considered. Now is the time to encourage healthy lifestyle choices in your child. Liposuction is not a quick fix and as a surgical procedure, carries certain risks.
NO. I would not perform this even with parenetal consent as it is an ethical issue as well as legal. There is no reason to perform liposuction on someone under the age of 18. I believe most patients are not mature enough to understand the risks at this age.