While most of this is valid (how dare a space opera expect me to suspend disbelief!), I think there is a basis for such a compactor to exist in the first place.
It stands to reason that a smaller vessel like a Star Destroyer, it is not logistically challenging to move the trash to an airlock for ejection.
On something so enormous as the Death Star, however, it might be so difficult to move the trash around that it's significantly more efficient to compact it before transport to the surface.
Also, a ship as small as a Star Destroyer doesn’t have to worry about issues that a Death Star might - it might make sense that the weight and balance of the Death Star has to be carefully controlled or it could get lopsided; meaning they don’t eject trash and instead compact it to be put on supply ships that just dropped off equal weight.
My biggest question that I don’t think has any plausible answer is the same as his first question: why is the trash system connected to the (presumably unobstructed) in-station ventilation? There is no feasible explanation.
It stands to reason that a smaller vessel like a Star Destroyer, it is not logistically challenging to move the trash to an airlock for ejection.
On something so enormous as the Death Star, however, it might be so difficult to move the trash around that it's significantly more efficient to compact it before transport to the surface.