Can we create interface protected or private if yes then how they will be implemented with a class?

Yes.
The usual rules apply as if you were declaring a class as within an existing class:

public class MyOuterClass
    {
    private void butCreate_Click(object sender, EventArgs e)
        {
        MyInterface mc = new MyClass();
        }
    public class MyClass : MyInterface
        {
        public void MyMethod()
            {
            throw new NotImplementedException();
            }
        }
    private interface MyInterface
        {
        void MyMethod();
        }
    }

The interface can be accessed by any classes defined within the outer class.