First things first: are you building locally, or do you use Phonegap Build?
I am using PhoneGap
If you are using the PhoneGap CLI, the PhoneGap project structure is taken care of for you. That is the CLI will create the basic structure automatically (such as "www" folder), and then as you add platforms and plugins it will take care of adding those structures as well.
Note: if you are having problems with the CLI, please share what commands you are using.
If you aren't using the PhoneGap CLI, please be specific as to what you're doing to create your projects and how you're testing them on devices.
What you do in your "www" folder, however, is entirely up to you. PhoneGap really doesn't have any requirements there, other than that you specify an HTML page from your "www" in your config.xml file so the app can start.
The CLI doesn't specify much of anything with regard to splash screens and icons, but I usually put those in a `res` folder as a sibling of `www`.