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
For the moment, if we look in our Windows phone Dev account and the W8 app Dev account you have no possibility to interconect the app versions targeting different devices. There are some rumours about that becoming available, but for now its not possible even if the app developer wanted so.
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.
Check for this icon in the app description, it means you can use the same app on both windows phone and windows 8, no need to purchase the same app twice