I want to ask if there are any differences when I develop metro style apps for Intel based processors devices or for ARM based processors ?
Are there limitations in code? Or do some APIs not work? Or can I write only one Windows 8 metro style app and run it on both?
If you're using C#, you can compile for both platforms without jumping through any special hoops. Only if you use libraries with specialized platform-dependent code (which aren't that many nowadays) you need to be careful.
In the API, I haven't come across functions that were restricted to one of the platforms either.