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.
- 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.
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 mean the head of state of the Roman Empire (among other heads of state); it implied something universal: he was