The Gym Teacher is descended from an alternate universe version of Major ArmstrongOne that fought in World War II and is famed for punching out his enemies.
Yugo's nightmare about getting paid the wrong way is a foreshadowing of something much more pleasant.Just replace the calf with Aki, and there you have it. The dialogue doesn't even have to change!
This universe is the one Edward Elric and Hohenheim land in at the end of the 2003 anime adaptation and Al ends up in in the movieWe may meet Ed's Grand/Great grandchildren at some point in the story, and they will be friends of Hachiken's in either the present or the past. They will also be very good at science. Also, in this universe, Ed and Al failed their attempt to find the atomic bomb and change the course of history, which is why this version of Japan is just like ours.
The cause of why Aki was crying at the beginning of the Autumn Arc was because of AyameIchiro and Aki were really good friends since childhood, so it may have been natural for Aki to have some concern over Ichiro's well-being. But after the death of Ichiro's father, the Komabas pretty much ended up with a lack of manpower and struggling for money. However, the Minamikujous have the opposite problem: A lot of money, but no more land. Thus, at some point between the end of summer break and the beginning of the fall semester, Ichiro may have been bethrothed to Ayame, and that's the reason why Ichiro can no longer have a girlfriend. Aki, thinking of her own imminent future of inheriting her family's farm, knew that she may have to find a husband soon...or have someone else do that for her. Knowing that she won't be able to fulfill her dreams of having a horse-related job, she cried.