1. Forbid the mentally ill to own guns of any kind.
No. Like others have said, "mental illness" is pretty vague, and could easily be abused by politicians, gov't officials, and law enforcement. Are you a member of the Tea Party? You must be mentally ill. Do you have more than 100 rounds of ammunition? You must be mentally ill. Do you openly oppose the president and his policies? You must be mentally ill. No guns for you.
2. Forbid those who have been found guilty of violence against fellow citizens from owning guns.
We already have laws for that.
3. Make illegal the purchase and ownership of armor piercing bullets.
No. Again, its how you define what an armor piercing bullet is.
What type of core(steel, lead, something else)?
Kinetic force at a certain distance
Piercing body armor(soft armor or hard armor plates)?
Piercing vehicle armor?
4. Make illegal any ammunition clips greater than 10 rounds. (Exception could be in place for gun ranges)
Absolutely not. And don't give me the "you don't need magazines that hold more than 10 rounds" argument. With all due respect, who are you to say what I need or don't need? Last time I checked, its called the Bill of Rights, not the Bill of Needs.
5. Make laws that punish gun owners if their own registered guns are used to commit crimes.
No. If somebody steals your car and commits a crime with it, do you go to jail? We already have laws about using a gun in a crime.
6. Closing the gun show loophole.