You can use whatever text editor you want. Eclipse is one of the supported IDEs by Google. It is used to build your Android app.
You can use Phonegap Build if you want. Phonegap Build will compile your code for you. You should use this template here for your code to be run through Build.
The easiest way to use Build is to place your code in a Github Repo. Then create/login to your Build account. Then select to create an app. Build will ask you to either input your gitup link (if you added your github account info to your build account there will be a drop down you can select from) or to upload a zip file.
Build will ask what platforms you want to build for ios, android, or windows. You need a ios certificate if you want to build for ios. Android will build without a certificate. You will need to add a certificate if you want to deploy to the market.
Build will also ask if you want to enable debug and hydration. For debug you will need to add the debug plugin to your project. When you run your app on your phone you can click debug and use weinre. Hydration allows you to update your code without re-downloading your app. If you update your code and rebuild the project the next time you open your app on your phone it will ask if you want to update your app.