Method Within A Method

If by nested method, you mean a method that is only callable within that method (like in Delphi) you could use delegates.

public static void Method1()
{
   var method2 = new Action(() => { /* action body */ } );
   var method3 = new Action(() => { /* action body */ } );

   //call them like normal methods
   method2();
   method3();

   //if you want an argument
   var actionWithArgument = new Action<int>(i => { Console.WriteLine(i); });
   actionWithArgument(5);

   //if you want to return something
   var function = new Func<int, int>(i => { return i++; });
   int test = function(6);
}

Yes, when C# 7.0 is released, Local Functions will allow you to do that. You will be able to have a method, inside a method as:

public int GetName(int userId)
{
    int GetFamilyName(int id)
    {
        return User.FamilyName;
    }
    
    string firstName = User.FirstName;
    var fullName = firstName + GetFamilyName(userId);

    return fullName;
}

Note that public (and similar modifiers) are not supported C# programming guide:

Because all local functions are private, including an access modifier, such as the private keyword, generates compiler error CS0106, "

This answer was written before C# 7 came out. With C# 7 you can write local methods.

No, you can't do that. You could create a nested class:

public class ContainingClass
{
    public static class NestedClass
    {
        public static void Method2()
        {
        } 

        public static void Method3()
        {
        }
    }
}

You'd then call:

ContainingClass.NestedClass.Method2();

or

ContainingClass.NestedClass.Method3();

I wouldn't recommend this though. Usually it's a bad idea to have public nested types.

Can you tell us more about what you're trying to achieve? There may well be a better approach.