Is it possible to use native Win API functions in Mono through Wine? Are there some additional libraries for interactions between Mono and Wine?
This will only work if you install and use the Windows version of Mono inside the Wine environment. No additional libraries should be needed. However, P/Invoke that affects the Windows Forms GUI likely won't work, because Mono's Windows Forms doesn't actually wrap native controls, but instead is implemented using fully managed code.
There's probably a better way to do what you want, if you could be more specific.