Yes, we can create a parameter less static constructor for a static class. It is used to initialize static members of the class. Static class must have all members as static.

Yes,We can create Static constructor to Static Class but we can not create instance constructor to static class.

Ofcourse we can create the Static constructor without any access modifier. Please take a look on below eaxmple

class Program
{
static void Main(string[] args)
{
MyStaticClass.printResult();
Console.ReadLine();
}

}

public static class MyStaticClass {
public static int num;
static MyStaticClass()
{
num = 1000;
}
public static void printResult()
{
Console.WriteLine(num);
}
}

class Program
{
 static void Main(string[] args)
 {
        sClass.printMethod();
 Console.WriteLine(sClass.num1 + sClass.num2);
 Console.ReadLine();
 }
}
 static class sClass
{
 public static int num1;
 public static int num2;
 static sClass()
 {
        num2 = 10;
 Console.WriteLine("static constructor print");
 } 
 public static void printMethod()
 {
 Console.WriteLine("it is printing from the static print method");
 }
}

static class sClass
{
public static int num1;
public static int num2;
static sClass()
{
num2 = 10;
Console.WriteLine(“static constructor print”);
}
public static void printMethod()
{
Console.WriteLine(“it is printing from the static print method”);
}
}

class Program
{
 static void Main(string[] args)
 {
        sClass.printMethod();
 Console.WriteLine(sClass.num1 + sClass.num2);
 Console.ReadLine();
 }
}

Yes , we can create constructor of static class but we cant create static constructor with parameter. in short static constructor is parameterless constructor and we just create static constructor once.