Are all the additions to C# for version 4 (dynamic, code contracts etc) expected to run on the current .NET CLR, or is there a planned .NET upgrade as well?
C# 4 will require the .NET 4.0 CLR.
Well, .NET 4.0 will require CLR 4.0; however, it is a little harder to answer what parts of C# 4.0 will work on .NET 2.0/3.x. We can hope that VS2010 will still be multi-targeting(I don't have the CTP "on me" so to speak, so I can't check...). But some of the language features don't seem hugely tied to the runtime (named parameters, some of the COM changes such as "ref") - so I can't think of a good reason why they wouldn't be available when talking to .NET 2.0/3.x. I haven't checked, though.
However, as with C# 3.0, some of the features are tied to the runtime - in particular
I need to dig out the CTP and have another play, methinks...
You don't have to wait for 4.0 to use Code Contracts as it runs on .NET 3.5, the download link for the academic preview release is here.