There were no emperors when the Julian calendar was created, during the Roman Republic (even though Caesar was de-facto proto-emperor at this point), and it was based on the Egyptian calendar which had 12 months. The Roman calendar was crap and had to be manually tweaked every year by the Pontifex Maximus (Caesar), and he had been inspired by the Egyptian calendar during his time there with Cleopatra.

The only months named after emperors are July and August.

I'm not entirely sure about Roman times specifically, but the number 12 was used a lot more in the past (hence words like "dozen") because it's easily divisible by 2, 3, 4, and 6, and doesn't have nonsense like 10/3 (well, 12/9, but who does that?)

The old Roman calendar had 10 months, which is why "December" comes from Roman "deci" for 10. Herp derp. IIRC they could add an extra "leap month" decided manually, or something. I'd have to look it up how it worked exactly. It was pretty complex and irregular, which is why it was replaced with what we have now. Aside from one minor bugfix it's worked pretty well for about 2,100 years.

Janus is a god, not an emperor. February is named after a purification ritual, not an emperor. March is named for Mars, a god, not an emperor. April’s etymology is unknown but we can be confident it wasn’t named after an emperor. July is named after Caesar, August after the man once known as Octavian.

February.