Thank you for refining the code and enhancing my understanding about Macro Recorder!
The code works absolutely fine.

The only issue I find is after having a drop down menu in cell R19, if I select any other value in cell J19 other than Single Parent Family, the validation list still exist in the cell R19, which prevents to enter anything new in the cell R19.

This issue is solved by just putting a line in the end of every "elseif line". This is highlighted in the code below..

Code:
Private Sub Worksheet_Change(ByVal Target As Range) '   https://excelfox.com/forum/showthread.php/2624-Drop-Down-Menu-with-Multiple-Conditions?p=14873&viewfull=1#post14873
    If Target.Address = "$J$19" Or Target.Address = "$J$19:$P$19" Then  '  we need  "$J$19:$P$19"  to make macro work on  Delete  probably because of merged cells
    Dim RngTgt As Range: Set RngTgt = Target
        If Target.Address = "$J$19:$P$19" Then Set RngTgt = Range("J19")
        If RngTgt.Value = "" Then
         Let Application.EnableEvents = False
         Let RngTgt.Value = "(Select Here)"
         Let Range("R19").Value = ""
         Let Application.EnableEvents = True
         Let RngTgt.Font.Color = 10855845
             Range("R19").Validation.Delete
             Range("R19").ClearComments
        ElseIf RngTgt.Value = "Nuclear Family" Or RngTgt.Value = "Joint Family" Then
         Let Application.EnableEvents = False
         Let Range("R19").Value = "(Remark if any)"
         Let Application.EnableEvents = True
         Let Range("R19").Font.Color = 10855845
         Let RngTgt.Font.Color = 6751362
             Range("R19").Validation.Delete
             Range("R19").Select
             Range("R19").ClearComments
        ElseIf RngTgt.Value = "Single-Parent Family" Then
         Let Application.EnableEvents = False
         Let Range("R19").Value = "(Select Reason for Single-Parent)"
         Let Application.EnableEvents = True
         Let Range("R19").Font.Color = 10855845
         Let RngTgt.Font.Color = 6751362
            With Range("R19").Validation
              .Delete
              .Add Type:=xlValidateList, AlertStyle:=xlValidAlertStop, Operator:= _
              xlBetween, Formula1:="Expired,Divorced,Break-Up,Abandonment,Enter Reason Manually"
              .IgnoreBlank = True
              .InCellDropdown = True
              .InputTitle = ""
              .ErrorTitle = "Error!"
              .InputMessage = ""
              .ErrorMessage = "To enter the reason manually, please select the option 'Enter Reason Manually'"
              .ShowInput = True
              .ShowError = True
            End With
             Range("R19").Select
             Range("R19").AddComment
             Range("R19").Comment.Visible = False
             Range("R19").Comment.Text Text:="Reason for Single-Parent"
        ElseIf RngTgt.Value = "Uncategorised" Then
         Let Application.EnableEvents = False
         Let Range("R19").Value = "(Please Specify the Case)"
         Let Application.EnableEvents = True
         Let Range("R19").Font.Color = 10855845
         Let RngTgt.Font.Color = 6751362
             Range("R19").Validation.Delete
             Range("R19").Select
             Range("R19").ClearComments
        End If ' end of all values of J19 to  result in actions
    Else  ' Target is not cell J19  ( or  J19:P19 )
  End If
    If Target.Address = "$R$19" Then
        Let Target.Font.ColorIndex = xlAutomatic
        If Target.Value = "Enter Reason Manually" Then
        Target.Validation.Delete
        Target.Value = ""
     Else
    End If
   Else  ' Target is not R19
 End If
End Sub

I'm surprisingly happy to see some changes in the macro, provided by you, which I really wanted but didn't know how to do that.
For example, this long code

Code:
Range("R19:Z19").Select
      With Selection.Validation
        .Delete
        .Add Type:=xlValidateInputOnly, AlertStyle:=xlValidAlertStop, Operator _
        :=xlBetween
        .IgnoreBlank = True
        .InCellDropdown = True
        .ShowInput = True
        .ShowError = True
      End With
is simply written in one line, as
Code:
Range("R19").Validation.Delete

__________________________________________________ __________________________

4. On clicking this cell "R19" a drop down menu appear with 5 option - "Expired" "Divorced" "Break-Up" "Abandonment" "Enter Reason Manually"
But that does not happen. If I click...
This line shows only the partial picture of the whole story. Hence, I think, it would be the reason for the misunderstanding.

The real story is here, which you have already solved nicely...
The drop down validation list in cell R19 is produced when the value “Single-Parent Family” is selected in cell J19
If that drop down list is present in cell R19 , and “Enter Reason Manually” is selected from that drop down list in R19, then the drop down validation list in cell R19 is removed.
The final line is just one...
Thanks a lot!!