One that implements the published specification for the platform/language? Just like MS got burnt trying to knock off java with J++ if you make a C# like languages that is broken from the standard in fundamental ways they'll come after you.
No - they can't. They have not put any clause in the licensing term for neither C# or core libraries prohibiting you from extending those. Sun did that with Java. Microsoft put the equivalent of C# delegates and P/Invoke into their Java implementation. Especially the latter riled Sun, as it allowed MS to integrate Java much more efficiently on Windows than Sun could do on other platforms. Sun sued and won and MS walked away from Java and created J++ but eventually went all-in on C#
This time around you can add anything you want. There is no non-free, licensed test suite you'll have to pass and there's limitation on how you can extend.