Is it illegal to shoot someone on your property if they have threatened you?
A couple of weeks ago I was out with a girl and her brothers didn't like it. So today her oldest brother's friend threatened to kill me if he ever saw me again and that he knows where I live. Would it be illegal for me to threaten him with a gun if he comes on my property being that he threatened to kill me? And would it be illegal to shoot him if he punches me being that he's a black belt in martial arts?
1) It is NEVER legal to threaten another person with a gun. If you or another person are in danger AT THAT MOMENT, you could draw and, if necessary, use the gun; but to issue a threat to someone with a gun would potentially make you criminally liable.
2) Whether you'd be justified in shooting him if he punches you would depend on the circumstances--for instance, even though he's allegedly a black belt, are large, tough, etc. are each of you? Are you truly in danger from him, if he attacks you empty handed? Also, say he punches you once, then stops--you can call the police on him, but you can't shoot him if the attack is already over (google "Bernhard Goetz" or "Berie Goetz" or "New York Subway vigilante Bernie" to see what happens if you shoot after the threat is done.)
Legally, to deal with a threat against your life, the proper action is to inform the police and possibly also seek some sort of protective order. To deal with an assault once it's over, you likewise call the police. You only use deadly force in the middle of an assault that contains a legitimate risk of significant injury or death to yourself or another person.
Every person in this country has the right to defend himself or herself against unwarranted attack using what force is reasonable and necessary under the circumstances. In your question, the mere threats that someone threatened to kill you without brandishing a weapon such as a knife or firearm typically would not warrant the use of deadly force in return in that there is no threat of an immediate and physical injury to you.
You should immediately contact law enforcement about the "death threat" that you received from this girl's brother and issue a statement so a formal report can be made about the incident.
If the brother comes onto your property, you would not have the right to use deadly force against him unless he actually demonstrates that he intends to use or is likely to use deadly force upon you.
If he shows up on your property, you need to call law enforcement immediately. Threatening him with deadly force if he shows up on your property given his threats to you is an open ended question in that if no threatening gestures are employed, it is not recommended to threaten the use of a firearm by you.
If the brother assaults and batters you, then you have every right to protect yourself within reason from further injury. I suggest you consult with an attorney over what happened and the possibility of getting a restraining order against the brother from coming in close proximity with you.