Was C# compiler written in C++?

Yes, but there are plans to write a C# compiler in C#, which I believe was discussed in this podcast.

Yes.

The Mono C# compiler is written in C#.

Yes it was - as majority of CLR. If you want to see the internals of CLR and/or compilers I would strongly recommend Shared Source CLI from Microsoft (aka Rotor):

• Microsoft Download
• Wikipedia
• Shared Source Internals book

But, there is actually a compiler written in C#. I believe that Mono is written that way. Download Mono sources and find out for yourself.