How to duplicate layers without affecting the original?

In the image you showed every layer except the first one is a pre-comp.

If it is the properties of each precomped layer then using Essential Properties like David suggested will work.

But if it the content of each precomped layer you want to change you will have to duplicate the layer source in the project panel to reuse it.

1. Right-click on the layer in your timeline.
2. Choose Reveal > Layer Source in Project.
3. Duplicate the composition that is selected in the Project panel
4. Make changes to that duplicate as necessary.

It sounds like you want to use Essential Properties, which is one of my favorite AE features. It's incredibly powerful, and you should really the help article and watch some tutorials, but in short, you can create a source comp and promote certain properties so they're editable. You then drag an instance of that source comp into your timeline and you can edit the targeted properties without affecting the original comp or any other instances. https://helpx.adobe.com/after-effects/using/essential-properties.html