Yes: since at least around October or so, NuGet.exe (the command line) works just fine under Mono in Linux. This is all you need to create and install NuGet packages. MonoDevelop does not yet have integration equivalent to VisualStudio's, but that's not a big deal.

Yes, but you may have to start it with:

mono --runtime=v4.0 NuGet.exe

You can also create a NuGet.exe.config file (put it in the same directory as NuGet.exe) to the same effect:

  <configuration>
    <startup>
      <supportedRuntime version="v4.0" />
    </startup>
  </configuration>

Whether you need it will depend on which runtime is enabled by default in your Mono installation. This can vary by system.

Also, you may need a fairly recent version of Mono to run NuGet; there was a bug in Mono that prevented NuGet from running, which was fixed only a few months ago.