In What Situation I Should Use Static Function ?

Check my Article for Static Class and Method Details.
Basic C# OOP Concept[^]

Now lets focus on your question
So you are asking the differance between static method and Public Static Method

As you know if we declare class or static or method as static we need to create object for to access that methods.
We can directly access the static method usign there class
example Yourclass.YourStaticMethod();

if you declare only static method by default it will be as private so outside class cannot access that method.
If you declare the static method as public outside class can access that method.

see the sample console program below for static method and public static method.

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace ConsoleApplication1
{
    public class YourstaticClass
    {
        static void welcomewithprivate()
        {
            Console.WriteLine("iam in Private Static Clss Method");
        }
        public static void WelcomewithPublic()
        {
            Console.WriteLine("iam in Private Static Clss Method");
        }
    }
    class Program
    {
       
        static void Main(string[] args)
        {
            //This line will be as error due to private static method can not be accessed in another class
            //YourstaticClass.welcomewithprivate(); 
            // Public Static method
            YourstaticClass.WelcomewithPublic();
            

        }
    }
}

Quote:

A property declared as static can not be accessed with an instantiated class object

That's not true, a static property can be accessed from everywhere. It is true the opposite, a static method cannot directly access instance properties.

Quote:

but where i should use static?

You should use static method when the implemented functionality does not depend on particular instance state.

1.The static keyword is for accessing class members that belongs to the class itself rather than to a specific object.

For example you can use static properties to stores data that are used/shared in common by all objects of a specific class, like application settings.

And you could use static methods for methods that are shared in common by all objects and do not depends on the objects non static members. This static methods could provide utility features like string.Format() is doing in the case of system string class.

2.Regarding your 2nd question about public static , you know that public access is the most permissive access level and this is valid also for static members.

So if you need that a static property or method to be accessible form other classes that do not inherit the parent class of your static members, you have to make your static members public, otherwise you could use internal, protected or even private (in the case when your static members is used only internally in your class).