Self-defence includes defence of others in my country's law. Going away from that example, which was, by the way, investigated as murder, not self-defence.

What the hunter did is not "take justice in his hands" in that scenario, it was defending others, self-defence as you say your country sees it.

If a regime forbids you to spread the truth people should be aware of (from your perspection), is it bad to spread the truth? According to your definition, Edward Snowden did bad. According to common sense, well, depends on the person. But I quite admire him and consider it good what he has done.

Actually what he did isn't Bad, it's clearly another case of Whistleblowing and in a court of law, by a jury of his peers, he should have no problem to walk out as he indeed gave information that pointed to a vast overreach of the government, in defence of the Constitution's 4th Amendment and in turn in defense of his State, and all United States in turn.

Another good example. Just re-reading your definition and seeing this "One day, after years of violent abuse from her husband, she took the law into her own hands." If she was regularly abused both physicaly and psychically, I think it is correct she finally stood up for herself.

The point is that if you go an kill the husband After he abused you, in retaliation, you have taken the law into your own hands and do not care for Due Process, which would mean to file a sworn affidavit (statement of fact) and dragging his ass before a Grand Jury. The reason why you should not and cannot do that under the law is that you weren't defending yourself anymore, you were literally taking vengeance or revenge at that point, and she didn't stand up for herself, she took vengeance on him, standing up for herself can only happen through the law, or through the situation, and she wasn't in a situation of impending danger or anything like that, or it would be simply self-defense.

It is against the law, but imagine how long it would take if she announced it to cops.

The point is that she wasn't counting on the cops to come rescue her from an impending life-threatening situation, she bid her time and enacted the vengeance she deemed appropriate.

If she was not refused, it would probably take months to get rid of the man.

That's not how the law works, they don't bide their time as everything is of the precious time. If your law takes "months" to deal with this then there is no law.

And he would add on his insults --- Of course, the state is probably able to help her in like 3 days, but there is no certainity in that for her.

No, the law has a duty to respond Promptly and with necessary force, in the case of assault they're not sitting on their hands, after all, that's what they signed up for to respond to sworn affidavits expedited by the judge, and the husband would have a "speedy" trial (trial in less than 30 days) meanwhile there will be a court order to remove him from the premises, and generally incarcerated awaiting trial with a hefty bail.

And if she had to face years of humiliation from this man, it is far and justified murder from my standpoint

There is no justified murder.