There's a very real danger in going back in time and trying to over simplify the motivations of an individual. It's dangerous enough to try to over simplify an event, but trying to over simplify motivations and what went into them? That's going down an absurd path.

Caesar "overthrew" the Republic because he had to, because he wanted to, and because he did. There were plenty of cases of incident, there were cases of his ambition, and there were cases of the fact that it left him with the other option of death.

Caesar, we know for certain based on every piece of writing we have available, including his own, was an ambitious man. That's why apocryphal stories were built around him weeping at the sight of a statue of Alexander the Great. That's ostensibly why he invaded Gaul.

But to try to keep the answer as simple as possible to keep with the scope of the question, Caesar was also playing a dangerous game. Climbing high in social and political ladders paints you as a target to people who envy you, who feel that the little peg that they occupy on the ladder is next on your climb, to people that disagree with your politics and feel that you are a threat, and people who want to curry favor with all those other parties by stopping you. Even the very best men in the world will always accrue enemies on the climb to the top, because the higher you climb, the more limited the space, and the more people are trying to push each other off the hill, so be ready to push someone else off or else you're going to wind up at the bottom.

And once you get to a certain level it literally becomes a bloodsport. There's no bowing out, you are on the path to victory or you're on the path to a knife in your throat. Cicero gambled against Augustus and he lost and so Cicero was killed, and Cicero, from everything I've gathered, never even had any designs on amassing his own dictatorial power. But that's the game you play at the high political level.

So why am I stressing this so much?

To understand that Caesar, who was deeply ambitious and pushed himself and his men to the heights of their success, was now bristling with threats, real and perceived. He owed an outrageous sum of money back home in Rome, which were necessary debts to fund his conquest of Gaul. His loose triumvirate had frayed at the edges and was all but gone and there were a number of men of influence deeply disturbed by the amount of power he was accruing for himself, with no signs of being interested in stopping.

Caesar was also in a tenuous situation because so long as he was a magistrate in Gaul he was immune from prosecution. When Pompey, speaking ostensibly for the Senate, called on him to disband his armies and return to Rome he saw that as an imminent death sentence. He refused, because as long as you're armed you have a seat at a negotiating table. Pompey declared that Caesar was being insubordinate and accused him of treason.

In Caesar's mind he was backed into a corner. Submission was the end of his political career and very possibly the end of his life. Flight was defeat and there was nowhere else for him to go. He'd be hunted anywhere in the empire for defying the Senate and he was not the kind of man to go to the Successor Kingdoms and sell himself as a mercenary captain or general to the Pontics or Egyptians or Baktrians.

So he marched forward to seize Rome. There's a lot of emphasis on the Rubicon and rightly so for symbolic value, but let's not emphasize too much on that. The reason the Rubicon was of significance is because crossing it was a declaration of his intent to take the gloves off and throw down. He meant to go wrestle Rome away from the people who had put his back to a corner, if only to, by his own claim, insure that his life and dignity were preserved.

By crossing the Rubicon he also compelled the Senatorial (Optimate) faction into action. It was a definite and, I speculate here but I would say deliberate, attempt to force an escalation. If the Optimates backed down it's possible that Caesar never would have become dictator or it's possible that his dictatorship may have come much later. But when Pompey rallied his armies and fought in the civil war it changed the perspective of the conflict. Now a faction of the Senate was fighting a wildly popular general who had brought slaves and riches back from Gaul.

So what happens when you beat the Senate? What happens when the men of the Republic and all their wealth and people of character, realistically or symbolically, are defeated? Well it obviously leaves a massive power vacuum for one. Caesar, in defeating Pompey and driving leaders of the Optimate faction into suicide or submission essentially quashed the opposition to his ambition. Who was left to check that ambition and temper his rise?

So now you have a power vacuum and an ambitious man who now controls the negotiating table all by himself.

What do you suppose is going to happen? Asking him to be Cincinnatus 2.0 seems a little unrealistic to me.

Additional reading includes:

Tom Holland's Rubicon (Don't recommend it as an entry, the guy is so biased it makes me sick)

Anything by Adrian Goldsworthy with particular emphasis on The Complete Roman Army

Life of Caesar by Plutarch

De Vita Caesarum by Suetonius

And I highly recommend Commentarii de Bello Gallico and Commentarii de Bello Civilii by Caesar himself.

As always in history, it is nearly impossible to discover the motivations of a single human being. This is true with Caesar, even though we have an incredible amount of information about him (for the ancient world): His own histories of his Gallic and Civil Wars, contemporary letters to him from Cicero, speeches written before, during and after his dictatorship, later biographies and histories, coins he had minted and inscriptions from all across the Mediterranean attesting to his decisions. Despite all this information, scholars have long debated about what Caesar's intentions and goals were.

Later historians and biographers, like Plutarch, Suetonius and Appian, tended to believe that Caesar was aiming at tyrannical rule from early in his life (Plutarch, Life of Caesar chapter 4 provides an example). There are very few scholars who accept this these days; Caesar's career was actually fairly typical throughout his early years, and it's only when he achieved his consulship in 59 B.C. and then gained governorship of Gaul (first for five years, later extended to ten) that he began achieving massive wealth and power. Even so, at this stage it does not seem that he was actively seeking to destroy the Republic (though his enemies accused him of this), but he most likely simply wanted to be the first man in Rome. That is, he wanted to outstrip all other senators in wealth, prestige and power.

If Caesar wasn't on a quest for dictatorial power, then why did he engage in civil war and eventually declare himself dictator for life? In 51-50, Caesar's enemies (which came to include his former son in law, Pompey) began collaborating to ensure that Caesar would not be able to stand for consul while still governor of Gaul, and to in fact recall him from Gaul. Their purpose was to put Caesar on trial and convict him, exiling him and depriving him of the chance of getting another provincial command and therefore more wealth and power; magistrates who held imperium in the Roman Republic could not be put on trial, and so they did not want Caesar to succeed to another consulship straight after his governorship of Gaul. Things came to a head when the consuls passed a "senatus consultum ultimum" (the final decree of the senate) essentially creating a state of emergency directed against Caesar; tribunes who were loyal to Caesar tried to veto the decree, and were chased out of Rome. When Caesar crossed the Rubicon in January of 49, he claimed that he was doing so to protect his dignitas from his enemies, who were unfairly attacking it (we can loosely define dignitas as his standing and position as a Roman nobleman) and to protect the tribunician power from those who were seeking to destroy it (Caesar, Civil Wars chapter 6). So, in fact, Caesar claimed he was protecting the Republic from those who were attempting to destroy it; they were the ones who had subverted it by attacking him and the traditional powers of the tribunes of the plebs (see the recent article by Morstein-Marx on Caesar's defence of the tribunician power as a possible popular motive for the civil war). Of course, these declared motivations are very self serving, and there has been much debate over whether Caesar or his enemies were ultimately to blame for civil war.

Throughout the civil war, Caesar defeated his enemies and gradually accumulated more and more untraditional powers. He initially held the dictatorship for short periods of time; precedent for this could be found in the early Republic, and more recently with Sulla, who declared himself dictator for the purpose of restoring the Republic. By 44 Caesar had himself declared dictator perpetuo, essentially dictator without limit of time (not necessarily for life). He committed other unprecedented acts, such as putting his own face on coins while still alive, and he appointed consuls and praetors years ahead of time, dispensing with some elections. Yet it is unclear whether Caesar even now meant to "overthrow" the Republic. There is a story that Caesar was offered a crown by Marc Antony and refused it (e.g., Plutarch Life of Caesar 61). We know that this actually happened from contemporary references (though these escape me right now; I'll have to track them down later, but I think Cicero's Second Philippic might reference it). Later authors like Plutarch believed that this incident was engineered by Caesar; he had hoped that the populace would cheer when Antony offered him the crown, and thus he could declare himself king; when the offer proved unpopular, he pretended that he didn't want the throne. That's possible; it may also have been an act of political theatre by Caesar showing that he was not a monarch and emphasizing his position in a Republic. Ultimately it is not clear whether Caesar at this stage meant to overthrow the Republic; his long term goals seem to have simply been to go on another campaign (against Parthia) and accumulate more money and prestige. He certainly didn't know that by adopting his nephew Octavius in his will he would cause the foundation of a system of "emperors" called the principate nearly twenty years after his death in March of 44. But again, the motives of individuals can be impossible to recover...

For further reading: Check out Adrian Goldsworthy's biography of Caesar, which is meant for a non specialist audience; and also Morstein-Marx and Rosenstein's chapter on the Transformation of the Republic in the Blackwell Companion to the Roman Republic, which provides a nice overview of modern scholarly theories on the fall or transformation of the Roman Republic.

I'll throw some added details to the other two posts.

Within the senate were a bunch of senators that had no hope of achieving high offices (e.g. praetorship, consulship, the censor). These offices tended to be dominated by a small group of senators from very powerful families, the elite of the elite. This grouping was the nobiles, someone who had a consulship within their family. Because of this monopolization of offices, it was extremely difficult for anyone who wasn't a nobiles to get elected - Cicero's election was an anomaly and reflected his skills.

Within this group, dignity and honour was a zero-sum game. If I am elected consul and you are not then my standing rises while yours fall. This results in serious competition for offices and by the Late Republic, politics had become incredibly cut-throat (sometimes literally). So when someone like Caesar is placed with a situation where they either have to initiate a civil war or step down (and face the inevitable retribution from opposing factions), civil war tended to be the preferred option. At that level of competition to withdraw was unbelievable shame to you and your family. Caesar wasn't the first to go down this road: Sulla marched on Rome twice to protect his dignitas, Catiline attempted a coup to reclaim his family's honour with a consulship, Caesar was just following their precedents.

Another point I'd like to make is that it wasn't Caesar against the senate. It'd be more accurate to say it was Caesar's faction against the Catonian faction - to which Pompey had allied himself to because he feared that Caesar had surpassed him in glory (c.f. honour being a zero-sum game). Cato had been Caesar's opponent since he stood for consulship in 59 BCE and is partially responsible for the collapse of the Republic due as his intransigence. His obstructionism in the senate towards Pompey and Crassus (two political enemies) had forced them to band together with Caesar as the First Triumvirate. It should also be noted that the bulk of the senate, the pedarii, favoured a peace deal where both Pompey and Caesar both disbanded much of their forces but it was rejected by the Catonian faction.

To your specific questions, yes Caesar was ambitious - but every single nobiles was ambitious. Everyone of them would drop-kick a puppy if it would get them more votes. Every single one of them wanted to be top dog in Rome and leave their mark, Caesar ended up having the biggest teeth. As for reforming Rome, he knew there were problems. Sulla in 88 had taken Rome in a civil war and then rewrote the Republic to try to fix the problems (that he himself created when he initiated the civil war) but failed. Based on this precedence I fully expect that Caesar would have tinkered with the Republic (as Sulla did) to try to 'fix' Rome. The problem being Rome was pretty much unfixable at this point, the core problem being any successful general with an army had a shot at being the next Caesar or Sulla. The zero-sum honour rules meant that the other factions within the senate would try to prevent a general from accruing honours and destroy them politically - leading to another attempt to take Rome to 'protect one's dignitas'.