With regards to the garbage thing, yes it is a PIB, but then again, Japan doesn't have a lot of natural resources so they need to recycle everything that are recyclable.
Whereas in the west we take the "dump all in the garbage bin and let the single waste management figure it out" (usually just ends up in a big landfill; a luxury Japan doesn't have) it's the opposite approach in Japan: "separate the garbage and let multiple garbage agencies recycle them respectively."
So Tuesday would be plastics day, and the plastic waste management comes by to pick them up.
Wednesday would be burnable day and the burnable waste management comes by to pick them up.
Yes it sounds redundant, but in a way it's a good way to becoming more responsible to what things you throw out.