Question: Is there a way to change the visual keyboard-theme via C#?
Or at least, some way to edit its properties, like background color etc?

Answer: 
Except for the `InputScope` (to open a numeric only keyboard etc.) and overriding key presses, there is currently no way to change any part of the visual Windows Phone keyboard.
Nope, this is one of those things that cannot be changed by third party applications short of various hacks (which would not be allowed in the marketplace). In general if something is controlled by a user setting then an application will have no way of changing it. You can detect whether the user has selected the light or dark theme and change the colours in your application accordingly, but your application cannot change system settings.