I'm using Windows. I have installed Visual C# 2010, mono and MonoDevelop. I know that MonoDevelop can use either Microsoft's compiler or mono's compiler. How do I check which compiler is used by MonoDevelop? And how do I change it to other one?
You can see and change the active runtime for the current solution using the Project->Active Runtime menu, or the active configuration picker in the toolbar. These options will be invisible if you do not have any alternate runtimes installed.
Note that these two places to set it are slightly inconsistent - the toolbar differentiates between using the "Default" runtime, and using that same runtime explicitly. You can specify the default runtime in the MonoDevelop global options: Preferences->.NET Runtimes.
And of course, if you want to double-check, you can just look at the build output section in the Errors Pad and see what compiler it's invoking.