No you can't create plugins using C#. However, you can access the scripting API of InDesign using C#. So a better way to put it would be you can write scripts for InDesign using C#
Where did you download the SDK from? Look in the <sdkpath>/build/win/prj folder and you shall find the project files. See the screenshot below
Open the project file in Visual Studio(look for the exact version to be used for different SDK), build it and you shall get the plugin. Look into the docs folder for documentation on how to start the plugin development and build sample plugins.