I'll leave discussion of Caesar to someone else.

Fascism wasn't born in ancient Rome.

Fascism of course stems from the Roman “fasces,” a symbol of power through national unity.

That the term fascism comes directly from the Roman "fasces" is not exactly true. Fascio was at the time (1910-20) a generic name for an association that wanted to differentiate somehow from the socialist "leagues" - there were thousands of fasci before Mussolini even conceived becoming the leader of the fascist movement proper; they multiplied during the war as interventionist, assistance organizations or opinion groups. There were those of students, clerks, etc. Most notable the so called Fascio Parlamentare di Difesa Nazionale - an influence group created around a core of liberal economists and politicians in the aftermath of the dramatic Italian defeat of Caporetto, soon drifting towards more nationalistic positions, to contrast the neutralist forces that they believed over-represented in the Chambers.

But of course, you can move a step back and trace the term's popularity to the Sicilian fasci, an agrarian movement of "socialist" inspiration that had large following in the 1889-94. Around the same time a Fascio della Democrazia (democratic fascio) was created under inspiration of the Socialist leader A. Costa.

As you can see, the term itself carried almost no national connotate, as it was chosen by both socialists, land workers and authonomist forces in late 19^th Century Sicily - forces that had no special inclination to identify themselves with the Italian Nation or State.

He actually created fascism in the image of a new Roman Empire.

So, while Mussolini certainly remarked the affinity between his established Fascist Regime and the grand age of Rome, this was more or less a necessary connection - the idea of restoring Italy to its former glory (establishing a "Third Italy" after those of Rome and the Renaissance) had been a key point of the Risorgimento process - see of course G. Mazzini or V. Gioberti's works - that Fascism cannibalized attempting to turn the various Risorgimento heroes into fascist precursors. Thus the privileged connection with a glorious (better) past established by the Regime (one of the central features of fascist movements - see f.e. R. Paxton or S. Payne) took the form of displaying "roman" imagery; a connection that was also easier to exploit for foreign propaganda reasons, as the general imagery of "Rome" was well known in the Western Countries and a symbol such as the fasces had never fallen out of favor - even if mostly, I'd say, as a reference to the Roman Republic.

But then again Mussolini did not "create" Fascism out of nothing, as numerous fasci di combattimento (combatants fasci) popped up after the war, founded by veterans and former interventionists; with Mussolini acting as a godfather - literally, no reference to the mob - for the most notable, created in Milan on March 23^rd 1919. Mussolini did not in the beginning run the movement as a political party - delegating most of the direction to Cesare Rossi - as the fasci di combattimento appeared destined to failure, due to lack of leadership, funds, members and a miserable electoral performance. Only with the agrarian battles of 1919-21 against the socialist leagues the fasci, funded largely by land owners, were able to become the most influential mass movement in Italy. And only then Mussolini saw fit to take official charge of the movement with the foundation of the National Fascist Party in 1921. Its symbol: the fasces. Here again though, little is present in the original ideology that can be directly connected with Rome; the symbol itself was partly an opportunistic choice - the other imagery of the fasci, such as the knife or skull of the Arditi might have looked less reassuring - a symbol of socialist origin, rooted in republican values, hinting to a generic but glorious past, then taken up by the interventionist movement during the defining experience of a victorious war, it mirrored the evolution of the fascist movement itself and the narrative it wanted to create.

Rome was incredibly nationalistic

I have discussed a bit of the relation between Fascism and Nationalism here but I must remark that nationalism is a fairly generic word that is used to describe widely different historical an cultural moments. I would be very cautious of mixing Roman "nationalism" with any national feeling rooted in the institution of a modern national state.

Italian Nationalism was - at least that's what you would want to discuss in relation to Fascism - a political (really on opinion movement at the beginning) movement born around 1903-04 under the initiative of Enrico Corradini and soon Giovanni Papini and Giovanni Prezzolini. It became more "political" with the incoming war and the contribution of jurist Alfredo Rocco. It had a program focused on freeing the productive forces of the nation from the bounds of the parliamentary system (a foreign import), rejection of socialism and praise of burgeoise values, a re-framing of the Risorgimento ideals (especially the idea that Italy had a decisive role to play in the progress of mankind - so called italianismo), a somewhat aggressive foreign policy seen as a way to ensure freedom of action to productive forces; a reform of the core institutions of the Nation based on the idea of juridical State.

As you can see Italian Nationalism was very much and early XX Century movement; and so were the German volkisch theories that influenced the development of National Socialism, or the ideas of conflict between nations as a cultural/biological struggle between peoples...

In fact this was the ground Fascism was born on - its historical context - and to ignore it entirely looking for distant analogues, means ignoring those features that actually made Fascism a unique and peculiar phenomenon of the XX Century. That would only leave us with an empty name.

Edit: spelling and fixing a sentence

I returned here after my contribution to the nationalism discussion to correct some misconceptions in the question. I see at least two of those conversations already have gone in an unfortunate direction (one set of comments almost entirely eliminated by the vengeful mods - if I'm repeating things covered in the deleted comments I apologize). I hope my comment here won't be taken the same way.

Point 3 about Rome generally and point 2 about Caesar I'm afraid are off-base.

Hannibal pushed Roman manpower to its ultimate limit. Following the defeat at Cannae in 216 (the last of three major defeats Hannibal inflicted) Rome was in such need of soldiers that in fact its normal source of soldiers, its citizen population and its allies, could not supply the immediate needs and the Senate took the unprecedented step of enrolling a slave army under Ti. Gracchus (the grandfather of the famous tribunes Ti. and C. Gracchus). This is the only case in Roman history I know of that Rome used a slave army. The slave army served well for a while, but when Gracchus died they just sort of wandered off, and had to be rounded up again.

Following Punic 2, Rome turned its attention to wars in the Balkan Peninsula, which had begun as part of Punic 2 but which they now prosecuted more vigorously. We hear about reluctance of soldiers to serve in these wars, and to handle the popular outrage the Senate limited the obligation to serve to Romans who hadn't served in Scipio's African campaign. The depletion of Rome's capacity to field troops in the 2nd century is well known, traditionally attributed to the extinction of Rome's yeoman farmer citizens, but Rosenstein has made a fairly convincing case that the shortage of soldiers in this period wasn't because of a paucity of qualified citizens, but rather a general reluctance of that class to become involved in oversea wars that required many years abroad with little promise of loot. So to say Rome had no problem finding new soldiers, even against Hannibal, is more than a little off-base.

About Caesar's "fiercely loyal" army, he suffered a serious mutiny of at least the IXth, possibly including soldiers from other legions. Caesar himself didn't write about this mutiny, and the most important source, the history of Pollio, who was one of Caesar's officer's, has been lost, but that account seems to be the one Livy, Dio, and Appian used when discussing Roman mutinies. Whatever happened there became what a Roman mutiny looked like. Caesar also suffered at least two other munities over the course of his military career, so it seems rash to state that Caesar's troops were particularly loyal.

I did gather that the consul/dictator confusion has already been addressed.

Forgot to include that Julius Caesar also inflicted mass genocide and killed an estimated million people