I'm uncertain what you mean by module? The first gear displayed was a sliding idler gear very similar to the one displayed at the end of the video in the Toyota transaxle.

I'm sorry, I don't understand the question. Oil lubricates the gears.

Oil is for lubricating (and cooling) the inner bushing as it rotates on the steel shaft that fits through it - any time there's metal sliding on metal, oil is needed

Yes, I may have neglected to mention cooling. The holes are referred to as lubrication holes not cooling holes but we all know that the lubrication helps to remove heat. For most (not all) manual transmissions there is no lubrication cooling mechanism so cooling of the lubricant is not prioritized. If the components are well lubricated the friction is minimized along with the increase in heat. Synchronization causes the highest amount of heat from friction inside a manual transmission or transaxle.