To make a unique composition duplicate you need to duplicate the source too. the source is in the project panel. Then you replace the duplicate precomp layer (in the timeline) with duplicated source (in the project window). if you have a comp with nested precomps you will have to duplicate them in the project window as well.
The common practice to create unique Comp structure is to duplicate the master comp in the project window, open it, duplicate the precomps in the project window and replace them with the ones in the duplicated master comp.
there is also an option to import the project to itself and you will get unique comps in the imported project.
another option would be the script True Comp Duplicator.
Thats very helpfull.
This is a common question on all AE forums. You need to study up on how AE works. Anything in the timeline can be duplicated but this does not change the original resource. Anything in the Project Panel may be duplicated but this does not change the anything that is in the asset. If you duplicate a comp in the Project Panel and you want to change anything inside that comp you need to also change what is included. If it is a nested comp with text then you need to duplicate that nested comp and change what's inside the duplicate.
Spend some time with the basics and you'll get the hang of the program. When you get lost try using the search help field at the top right corner of AE. It is usually any times better at pointing you to good techniques and workflows than Google will ever be.