Is the description of the death of Rabbi Akiva's disciples in Halacha logical and realistic?

Peace and blessings!
Is the description of the death of Rabbi Akiva's disciples in Halacha logical and realistic?
I would like to ask about the historical basis for the reason for the custom of mourning during the days of the Sefira except for Lag BaOmer (I will refer to the Ouch 30 573 at length for several methods). According to what the poskim wrote, the reason for mourning is because during that period 24,000 of Rabbi Akiva's disciples died (Yevamot 62:), and on Lag BaOmer they ceased to die (according to one explanation).
A. Apparently, Rabbi Akiva meant a "yeshiva" of 24,000 students. But that doesn't sound logical. Even today, it is technically impossible to maintain such a yeshiva, especially back then when the feeding, housing, and transportation capabilities were far behind today. So let's assume that he meant "graduates," meaning that during his years of teaching he had accumulated a lot of students, and at the time of the disaster they were already scattered throughout the country, immersed in various occupations.
on. How is it possible that 24,000 people died of such a disease in such a short time? The Gemara says that they died of "askareh." Let's assume that it was a contagious disease (in "Hebruta" it says that it was "death by suffocation due to inflammation of the throat"). Does it mean that the disease affected only them, and consumed everyone? How did it not affect their wives and children? The simplistic description is that there is a disease that rages in a very short time, and affects a very specific population in a very selective way, like a "plague of firstborns."
third. The Gemara says that they died before the assembly. Then the Rishonim found midrashim that are unknown to us, that they died only before the assembly was organized (and the Hidda (Responsa Tov Ein 6:18) made it difficult for us to accept our version because of these midrashim). Well, then they calculated and concluded that the reference was to Lag BaOmer. They also decided that if they stopped talking about dying, it was a reason for joy (and they already made it difficult for us to know what joy there was in that, after all, there was not one left).
The historical problem is that, according to many methods in the Shulchan Shulchan, we do not take the view that they stopped dying on Lag BaOmer, but rather that they stopped dying after 32 scattered days. That is, the students of the Re's died throughout the entire counting of days in leaps, on the day when Tachanun is said they died, and on the day when Tachanun is not said (Sabbaths and the days of Passover and Ra'ach) they did not die (and this is according to the Maharil), see the summary in "Bi'or Halacha" there. And in order to indicate that they stopped dying after 32 days close to the 19th of Shavuot, they chose to celebrate Lag BaOmer as a day of joy.
This is truly a historical miracle. After all, in the plague of the firstborn, it is said that the doorways of houses must be marked with blood, and since permission was given to the destroyer, he does not distinguish between the righteous and the wicked. And how here did the destroyer distinguish between a day on which Tahanun is said and a day on which Tahanun is not said, and kill only on that day?
And let's assume that this is what happened. Was there a "population authority" operating there that traveled throughout the Land of Israel, recording exactly on what day each student died?
Thank you very much.