To answer only the first part of the question: difference between PhoneGap and Intel XDK.
PhoneGap is a framework, that allows building multi-platform mobile apps from HTML and Javascript source, created and supported by Adobe. It is proprietary.
Cordova is open source version of PhoneGap maintained by Apache.
Intel XDK is IDE based on Cordova.
The difference in creating apps with Cordova(or Phonegap) and Intel XDK is that in the first case you type commands in prompt window and in the second you click on IDE buttons.
The result application is supposed to be the same.
