Can anyone explain how the CLR handles Static classes? Does the CLR create one singleton instance for handling static classes internally? If not, why do we have a static constructor in C#? (Per my understanding, we use constructors only for instantiating the class)
First of all there is no static class in CLR. CLR doesn't know anything about static class. It is the feature of C#.
Static classes are compiled into abstract as well as sealed class. Making it abstract prevent instantiation of it and sealed prevents inheritance.
Static classes are no special, it is just a simple class with all members static.
Is, CLR internally creates one singleton instance for handling static classes?
No, it is abstract and can't be instantiated.
If not why we have an static constructor in C#?
Static constructor will be called when type is first referenced or instantiated. It is used to initialize the static members of the class.