OK, about the epilepsy:
The conspiracy nuts have picked up on this issue, some claiming that Caesar willfully allowed himself to be assassinated, as he knew that his epilepsy was going to get him soon anyway, either by killing him or turning him into a slobbering fool, and he figured that being assassinated in the senate was a more statesmanlike way to go. However, I don’t think there’s any actual evidence for this.
Anyway, the supposed epilepsy is mentioned by several sources, most importantly Plutarch. It’s worth noting that Plutarch actually seems to downplay the whole issue, claiming that it did not hinder Caesar in the field, but rather made him hardier:
“For he was a spare man, had a soft and white skin, was distempered in the head and subject to an epilepsy, which, it is said, first seized him at Corduba. But he did not make the weakness of his constitution a pretext for his ease, but rather used war as the best physic against his indispositions; whilst, by indefatigable journeys, coarse diet, frequent lodging in the field, and continual laborious exercise, he struggled with his diseases and fortified his body against all attacks.”
Another story is that when Caesar was deified by the senate, he received his honors while sitting down, instead of standing up, as expected. This was widely seen as arrogant and disrespectful behavior, and apparently offended both the senate and the public. Plutarch relates that Caesar himself claimed that his epilepsy was the reason that he remained seated:
“But afterwards he made the malady from which he suffered, the excuse for his sitting, saying that those who are attacked by it, lose their presence of mind, if they talk much standing; that they presently grow giddy, fall into convulsions, and quite lose their reason.”
However, once again Plutarch goes on to downplay it, saying that this wasn’t the real reason, and that Caesar had in fact simply taken some bad advice:
“But this was not the reality, for he would willingly have stood up to the senate, had not Cornelius Balbus, one of his friends, or rather flatterers, hindered him. ‘Will you not remember,’ said he, ‘you are Caesar, and claim the honor which is due to your merit?’”
Plutarch does also state that Caesar had an epileptic seizure in the middle of the Battle of Thapsus, two years before his death, but he points out elsewhere that the seizures didn’t start until the end of Caesar’s life.
So, if we are to believe Plutarch, Caesar was indeed epileptic, but the condition must have been rather mild. As it happens, another historian, Cassius Dio, actually claims that Caesar remained seated in the senate not because of an epileptic fit, but to hide an attack of diarrhea!
The epilepsy is also mentioned by the historian Suetonius, who claims that Caesar had epileptic fits twice while on campaign, as well as by the historian Appian. Of course, Shakespeare also made a point of it “Julius Caesar”, based on the aforementioned historians, thereby adding to the popularity of the idea:
CASSIUS: But, soft! I pray you. What, did Caesar swoon?
CASCA: He fell down in the market-place, and foam’d at mouth, and was speechless.
BRUTUS: 'Tis very like: he hath the falling-sickness.
OK, so, after all that… was Caesar epileptic? Heck, yeah, probably. But perhaps not very.