Was killing Julius Caesar an act of justice?
This is a good question and there is no one right answer. If you look at the historical Caesar, there is a case to be made that he was aiming at something greater than anything else in the past. For example, he was dictator for life, which was never done before. Furthermore, he heaped on title after title. So, if a person was a staunch defender of the Republic, then I can see why he would consider killing Caesar an act of justice. Caesar would be a direct threat to Republican ideals.
On the other hand, no one really knows what Caesar was up to, since he was killed. If we look at things from Shakespeare's perspective, then I would say that Caesar was killed unjustly. He was not a tyrant nor did he want to be king. This is why Brutus is portrayed as a tragic hero. He was used by the other conspirators to aid in the killing of Caesar. In other words, Brutus was sincere. But in the end, Brutus finds out that he was used.
Depends, like most things, on your point of view. Brutus saw it as the only way to stop Caesar's ambition which was a major threat to Rome's current power structure. He loved Caesar as a man but killed him for his ambition because there was no other way to stop it. For Marc Antony it was not justice because even though he loved Caesar as a mentor, he saw it as a way to convince the people of Rome to destroy the assassins and thus gain his own share of the power of Rome.