Trying to integrate composer with an existing Cake 2.5 application

I have an existing CakePHP 2.5 project where CakePHP has been manually installed. I want to use the features of composer to manage the project's dependencies including Cake.

Right now, the project has a folder structure such as:

project_root/

 app/

   Config/

   Controller/

   Lib/

   Model/

   Plugin/

   Vendor/ [1]

     cakephp/ [2]

   View/

   webroot/

  composer.json [3]

 lib/ [4]

   Cake/

 plugins/

 vendors/

From my understanding of how composer works, it will install its dependencies to Vendor [1], and Vendor/cakephp [2] should have the latest CakePHP source defined on composer.json [3].

However, the project has the lib/Cake folder that also contains CakePHP source.

My questions:

1. This project is managed by git. What should I commit to git that won't break anything else? The production server is running off a git branch.

2. Should I remove the lib folder? [4]

3. In Cake's documentation here: http://book.cakephp.org/2.0/en/installation/advanced-installation.html

In the "Installing CakePHP with Composer", it mentions "Save this JSON into composer.json in the APP directory of your project.". How can I have an app directory if I'm still installing Cake? I got confused here.

Thanks 

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