The Mono community was essentially forced to re-implement .NET because no open source implementation was available. Customers have reported various mismatches, which are hard to fix because neither side can look at the code of the other side. This also results in a lot of duplicated work in areas that aren’t actually platform specific. The best way to build a cross-platform stack is to build a single stack, in a collaborative manner. Mono and .NET aren't one, but they'll be able to work together in an unprecedented way. There's Linux stuff in Mono that we would like to use (and vice versa).
To answer your last question: Yup.