I would consider older (e.g., 25).
For proof of emancipation, could be (1) military ID, or (2)(a) proof of ownership of a homestead (property on which you live and regarding which you pay taxes) or (2)(b) proof of rental payment on a property at an address in which an older voter is not also listed on the voter rolls.
"Adult activities" includes voting and buying any kind of gun. If you are too immature to own a gun (which includes getting a free photo ID), then you should not be voting, and vice-versa. Also, I would consider having a major medical procedure to be an adult activity, and so parental consent should be required unless the individual is emancipated from their family.
Although, I would consider lowering the minimum age for buying alcohol and cigarettes (go with the European model here), as long as the punishment for DUI's increases significantly.
As to punishment in the justice system, I would abolish the juvenile system for intentional/forcible felonies resulting in death when the perpetrator is over the age of, say, 8 years. All such people should be charged as adults. If they don't know by 8 that it is wrong to kill someone, they will never figure it out. If they want to defend on the basis of lack of mental capacity, they can do it like adults do, and the court can rule.