the layer I copied is not visible in the timeline of the new composition

It looks like the in-point is just displaced. When you copy and paste a layer the copy's in-point is placed at the CTI's (current time indicator) position. 

Your comps are very long. I hope you are not trying to use After Effects to edit a move. It is not a video editing app. It is an animation and compositing app designed to create shots that can be edited into a movie using an app like Premiere Pro.