What's a good approach to describing how Shakespeare presents different types of conflict in Julius Caesar? What are the main themes of conflict?
The basis of Shakespeare's play Julius Caesar is based upon the conflicts of those in his kingdom who, for one reason or another, do not want Caesar to be crowned king.
I can only answer one question, so I will identify the conflicts and related themes, discussing only one in depth.
Themes in Julius Caesar are whether it is justified for a king to be killed. This was an important moral debate, and one that Shakespeare wrote about in other plays such as Hamlet and Macbeth. Most people of Shakespeare's time believed it was a sin against God to kill a king, and that it disrupted the natural order of the world, causing terrible things to occur, for example, in nature.
Ambition is another theme in this story. Caesar is accused, after his murder, of being too ambitious, and this is the topic of Mark Antony's eulogy, delivered at Caesar's funeral. Mark Antony argues that ambition is hardly a crime if it refers to caring for others, as was the case with Caesar.
Civil war or civil disorder is another theme, something Elizabethans would have been quite familiar with, as England's history was filled with long years devoted to civil wars between the royal houses grappling for control and power, i.e. the War of the Roses (just to name one) [see Wikipedia source].
The theme of ambition is central to judging those in power that surround Caesar before and after his death. Caesar sees himself as something of a "god," and Brutus is manipulated by Cassius to align himself with those who want Caesar dead. The reasons Cassius provides Brutus with are not well-founded, but self-serving for Cassius. One conflict that emerges here is man vs. self, as Brutus struggles with whether or not he should help assassinate Caesar. Brutus' intentions are well-founded, but his actions are not truly justified.
When Caesar is accused of having been too ambitious, Mark Antony directs his remarks (at Caesar's funeral) to this perception. He denies the truth of it. Ironically, where Cassius and even Mark Antony are motivated by their own ambition, once again, Brutus is not.
Brutus' actions are driven by his need to protect his country's future, which he thought he was doing when he finally decides that Caesar must die. However, after the murder of Caesar, Brutus must face the masses—the mob—who want revenge for their leader's death. At this point, the conflict becomes man vs. society.
Continuing on in this line, Cassius' own ambition may be questioned, though it seems he was not as interested in furthering his own ends—which would not happen with Caesar's death—as much as simply wanting to wrest the power from Caesar's hands. This conflict is an example of man vs. man.
Though Mark Antony defends the dead leader against accusations of ambition—as if ambition were a horrific trait in Caesar (as Brutus insists)—Mark Antony is just as ambitious as any of the other characters, and it is he who will ultimately become one of the most powerful men in Rome after Caesar's death and the conclusion of the civil disorder that arises when Caesar is killed. As mentioned, this is ironic: Antony argues that Caesar was not ambitious in a destructive way and questions the validity of such a charge to warrant the great man's death, and yet, ambition serves him (Antony) well in the end. However, Antony is not a part of the assassination, and his conflict is simply to restore power to Caesar's heir, Octavius, and Antony himself (man vs. man).