What do these C++ code snippets do?

Question

#ifdef _DEBUG
    #define new DEBUG_NEW
    #undef THIS_FILE
    static char THIS_FILE[] = __FILE__;
#endif

Why define these tags?

CSortHeaderCtrl::CSortHeaderCtrl()
    : m_iSortColumn( -1 )
    , m_bSortAscending( TRUE )
{
}

What are the two functions after colon used for?

BEGIN_MESSAGE_MAP(CSortHeaderCtrl, CHeaderCtrl)
    //{{AFX_MSG_MAP(CSortHeaderCtrl)
        // NOTE - the ClassWizard will add and remove mapping macros here.
    //}}AFX_MSG_MAP
END_MESSAGE_MAP()

Are there any similar things in C# like this?

What's this used for?

virtual ~CSortHeaderCtrl();

Why set the destructor function to be virtual?

void CSortHeaderCtrl::Serialize( CArchive& ar )

When will this function be called?

Is this extended from parent?

By the way, when you want to extend a MFC class, what document you will read?

Since we don't know what function it has, what function can we override?

The following is the header file:

/* File: SortHeaderCtrl.h 

   Purpose:  Provides the header control, with drawing of
             the arrows, for the list control.
*/

#ifndef SORTHEADERCTRL_H
#define SORTHEADERCTRL_H

#if _MSC_VER > 1000
    #pragma once
#endif // _MSC_VER > 1000

class CSortHeaderCtrl : public
CHeaderCtrl { // Construction public:
    CSortHeaderCtrl();

    // Attributes public:

    // Operations public:

    // Overrides     // ClassWizard generated
    virtual function overrides
        //{{AFX_VIRTUAL(CSortHeaderCtrl)
        public:     virtual void Serialize(CArchive& ar);
        //}}AFX_VIRTUAL

    // Implementation public:     virtual
    ~CSortHeaderCtrl();

    void SetSortArrow( 
        const int iColumn,
        const BOOL bAscending );

        // Generated message map functions
    protected:     
        void DrawItem(LPDRAWITEMSTRUCT lpDrawItemStruct );

        int m_iSortColumn;     
        BOOL m_bSortAscending;

        //{{AFX_MSG(CSortHeaderCtrl)         //
        NOTE - the ClassWizard will add and
        remove member functions here.
        //}}AFX_MSG

    DECLARE_MESSAGE_MAP() };

//{{AFX_INSERT_LOCATION}} // Microsoft
Visual C++ will insert additional
declarations immediately before the
previous line.

#endif // SORTHEADERCTRL_H

Answer 1

Question 1: The DEBUG_NEW is probably so the 'new' operator records some extra information about where and when a block was allocated to help in detecting memory leaks, see this. The THIS_FILE[] static char array simple holds the current filename, probably used by the debug 'new'

Question 2: This is an C++ initialization list.

Question 3: The destructor is declared virtual because there are other virtual members and this is a derived class. The 'delete' operator needs to know the correct size of the object it is deleting, along with which actual desctructor to call, see this