I think we have break down your question, based on the background you supply
(Warning: long post - I actually know some things about this)
- Why was the the historical figure Julius Ceasar so important?
As a general he was responsible for several expansions of Roman rule that were upheld for hundreds of years, most notably Gaul (modern France, more or less)
He was popular among the soldiers common people (plebs) of the City and used that position to advance his political position, ie neutralize his political enemies and concentrate all power in his own hands. This marked the end of the Roman Republic as it stood for a few hundred years. From a modern perspective replacing a ‘republic’ with an ‘empire’ under a dictator/emperor may sound like a step backwards for a society, but keep in mind that this ‘republic’ was by no means a democracy in the modern sense, but an oligarchy where all money and power was in the hands of a very small class (the senators) who traced their family ancestry to Romulus & Remus and co.
The fact that he was a) popular among the common people and b) murdered by the once ruling elite surely helped his legendary status, but this should not be overestimated. Very few emperors in this period of Roman history died of natural causes, so to speak.
At that point in time however, he could still have ended up as ‘just another’ popular political leader who was murdered because of this. That’s where Octavian who restyled himself as Ceasar Augustus comes in. The nobles killed Caesar but lost the war …
- Why is/was the name ‘Ceasar’ so important?
While it was Julius Ceasar who had started the whole thing, it was Augustus who consolidated the new political constellation, using the name Ceasar to underline that he was working to continue his legacy. His function as head of state and boss of everything, which we now call ‘emperor’, was at the time commonly referred to as ‘princeps’ (first citizen) - which btw is the origin of the English word Prince. If you wanted to really insult Augustus or Julius, you’d call him ‘King’ (Rex) - the rough equivalent of calling a US presidential candidate a communist. And ‘dictator’, I might add, did not have the negative connotation of today but was rather neutral or even positive.
Anyway, after Augustus it became the tradition for emperors to name themselves Ceasar.
- How did the name ‘Ceasar’ (Kaiser, Czar) come to signify the highest position among nobles in medieval and early modern Europe?
First thing you have to understand is the world view of people in Roman and medieval times: Caesar/Princeps/Emperor did not just signify the head of state of the Roman Empire (as in: among other heads of state); it implied universal leadership: he was THE Emperor. The known world was either directly ruled by Rome, a tributary to Rome or Barbarian country. This notion became so firmly established in the minds that the Frankish king Charlemagne (8th-9th century AD) after conquering most of Western Europe felt he had to have himself crowned Emperor/Ceasar/Kaiser by the pope in … yes, Rome. (The Roman Empire had become Christian around the 4th century AD) Thus Charlemagne established the Empire which for centuries to come was referred to as the Holy Roman Empire. Even Napoleon, some 1000 years later crowned himself Emperor in Rome for the same reason. Charlemagne’s ‘empire’ was however soon reduced to modern day Germany, Austria and Northern Italy and the Emperor lost much of his power to the lower regional nobility and the Emperorship was even abandoned for a time until German unification in the 19th century. But nonetheless: the last German Emperor, who was deposed at the end of WWI, was still the traditional political heir of Ceasar and Augustus.
But wait, there was a second Ceasar in Moscow, the Czar!
Yes, there are traditionally two Emperors. This was a result of the cultural and political divide between the Western and Eastern parts of the Roman empire, which were in the end separated for good. After the so called ‘end’ of the Roman Empire in the early Middle Ages, there still remained an Eastern Roman emperor based in Constantinople/Byzantium (now Istanbul, Turkey) ruling over what’s usually called the Byzantine Empire. This came to an end far later, in the 15th century when the Turks conquered Constantinople. I’m less familiar with the details, but somehow the Prince of Moscow picked up the crown and styled himself Czar.