We could eat it on a special day which was once a month, so we always looked forward to theat day.¶

"the" is fine grammatically, but it can be used for any day
"that" goes with "special" and "once a month" to highlight that day

I also liked a fried bread served on normal days.

We don't say "a bread." Maybe the reason we don't is that bread is usually cut into pieces, so we say "a piece of bread" or "a slice of bread."

It was seasoned with sweaet soybean flour, and we always scrambled to get them in my classroom.

Sweat forms on your skin you when you are very hot.
If scrambling refers to all the students rushing and pushing to get the fried bread, then you could say "scrambled to get them."
"Scrambled" can also mean mixed. "Scrambled eggs" are beaten, so the yellow and white are mixed before the eggs are cooked in a pan.

What wais your favorite type of school lunch?

My favorite type of school lunch wais sushi.

We could eat it on special day which was once in a month, so we always looked forward to ithe day.

I also liked a fried breads served on normal days.

It was seasoned with sweat soybean flour, and we always scrambled them in myour classroom.