If I buy a Windows Phone 8 app and there is the same app for Windows 8 as well, will I be allowed to download the same app to this device (Surface/PC) too? Same goes for buying a W8 app and getting the WP8 app if it exists
With Windows 8.1 and Windows Phone 8.1, Microsoft is introducing the concept of Universal Apps. A developer has to enable this feature for his apps, and then even in-app purchases can be shared between the desktop, tablet and phone (at some point probably even your Xbox).
A nice, detailed write-up can be found at WPCentral.