Those weren't my tl notes lmao, they were in the chapter to begin with, calling them horrible and all.
Makegumi backpack literally means failure's backpack, it's calling those people a failure, like the note itself explains, the parent lottery is just dehumanizing and mean, and the kataoyapan is just a kinda mean way to jokingly refer to poverty in single parent households. It literally means "single parent bread" and refers to discounted value packs of bread.
I felt each box explained it enough on their own, and a tl note from me would just be repeating that.