以下是在WIN7 64 ，delphi xe 10.3 以下成功运行：

运行界面：

代码

unit Unit1;

interface

uses
  System.SysUtils, System.Types, System.UITypes, System.Classes, System.Variants,
  FMX.Types, FMX.Controls, FMX.Forms, FMX.Graphics, FMX.Dialogs, System.Rtti,
  FMX.Grid.Style, FMX.StdCtrls, FMX.Grid, FMX.Controls.Presentation,
  FMX.ScrollBox, FMX.Memo
  //,System.Types
  ,FMX.Header     //THeaderItem
 // ,System.UITypes  //[TFontStyle.fsBold]

  ;

type
  TForm1 = class(TForm)
    stringgrid1: TStringGrid;
    A: TStringColumn;
    B: TStringColumn;
    C: TStringColumn;
    D: TStringColumn;
    E: TStringColumn;
    Panel1: TPanel;
    StyleBook1: TStyleBook;
    CornerButton1: TCornerButton;
    CornerButton2: TCornerButton;
    CornerButton3: TCornerButton;
    procedure FormCreate(Sender: TObject);

    procedure AppendClick(Sender: TObject);
    procedure DelClick(Sender: TObject);

    procedure InsertClick(Sender: TObject);
    procedure stringgrid1DrawColumnHeader(Sender: TObject;
      const Canvas: TCanvas; const Column: TColumn; const Bounds: TRectF);
    procedure stringgrid1HeaderClick(Column: TColumn);
    procedure CornerButton2Click(Sender: TObject);
    procedure CornerButton1Click(Sender: TObject);
    procedure CornerButton3Click(Sender: TObject);
  private
    { Private declarations }
    procedure addRow(const row:integer);
    procedure delRow(const row :integer);
    procedure insertRow(const row:integer;val:array of Variant);
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

implementation

{$R *.fmx}

procedure TForm1.AppendClick(Sender: TObject);
var
temprow :integer;
begin
     for temprow := 0 to stringgrid1.RowCount-1 do
     begin

       if stringgrid1.Cells [0,temprow].IsEmpty then
       begin

         break;     //此处不能用EXIT 哟
       end;

     end;
    addRow(temprow);

end;

procedure TForm1.addRow(const row:integer); //在末尾追加
var
col,Selrow:integer;
begin
    selRow:=row;
    for selRow:= selRow to selRow   do
        for col := 0 to stringgrid1.ColumnCount-1  do
        begin
         stringgrid1.Cells[col,selRow]:=selRow.ToString  ;
        end;
end;
procedure TForm1.delRow(const row :integer);
var
col,Selrow:integer;
temprow,rowcount:integer;
begin
   for temprow := 0 to stringgrid1.RowCount-1 do
     begin
       if stringgrid1.Cells [0,temprow].IsEmpty then    //第一列为空，则表明后面全部为空行。
       begin
         rowcount:=temprow ;
         break;     //此处不能用EXIT 哟
       end;
     end;
  Selrow:=row;
  for Selrow := Selrow to (rowcount)   do  //当前行开始，把后面的数据覆盖当前行；
      for col := 0 to stringgrid1.ColumnCount-1  do
      begin
       stringgrid1.Cells[col,Selrow]:= stringgrid1.Cells[col,Selrow+1] ;    //用后面的数据覆盖当前行；
      end
end;
procedure TForm1.insertRow(const row:integer;val:array  of Variant);
var
col,Selrow:integer;
c,temprow ,rowcount:integer;
beGIN
   //row 是选中行号
  for temprow := 0 to stringgrid1.RowCount-1 do
     begin
       if stringgrid1.Cells [0,temprow].IsEmpty then
       begin
         rowcount:=temprow ;
         break;     //此处不能用EXIT 哟
       end;
     end;

  for c:=rowcount+1  downto row do
     for col := 0 to stringgrid1.ColumnCount-1  do
        begin
         stringgrid1.Cells[col,c]:= stringgrid1.Cells[col,c-1] ;
        end ;  //上述是完成从当前行各自后移一行

    //row 是选中行号
    stringgrid1.Cells[0,row]:=val[0] ;
    stringgrid1.Cells[1,row]:=val[1];
    stringgrid1.Cells[2,row]:=val[2] ;
    stringgrid1.Cells[3,row]:=val[3] ;
    stringgrid1.Cells[4,row]:=val[4];

end;
procedure TForm1.stringgrid1DrawColumnHeader(Sender: TObject;
  const Canvas: TCanvas; const Column: TColumn; const Bounds: TRectF);
  var
  Header: THeader;
  HeaderItem: THeaderItem;
  I: Integer;
begin
    Header:= Theader((Sender as  tstringgrid).FindStyleResource('header'));
    if Assigned(Header) then
    begin
        for I := 0 to Header.Count - 1 do
        begin
          HeaderItem:=header.Items[i];
          HeaderItem.Font.Size:=12;
          HeaderItem.Font.Style:=[TFontStyle.fsBold ,TFontStyle.fsItalic, TFontStyle.fsUnderline];
          HeaderItem.TextSettings.HorzAlign := TTextAlign.Center;
          HeaderItem.StyledSettings := HeaderItem.StyledSettings - [TStyledSetting.Size, TStyledSetting.Style];
        {
        HeaderItem.Font.Style := [TFontStyle.fsBold];
         property Style: TFontStyles read GetStyle write SetStyle stored False;
         TFontStyle = (fsBold, fsItalic, fsUnderline, fsStrikeOut);
         TFontStyles = set of TFontStyle;
         }

        end;  //for I := 0 to Header.Count - 1 do
        Header.Height := 24;

    end;  //if Assigned(Header) then

end;

procedure TForm1.stringgrid1HeaderClick(Column: TColumn);
VAR
columnS:STRING;
begin

//SHOWMESSAGE(inttostr(chr(column.Name))) ;
//  columnS:= column.Name;
 CASE column.Index OF
  0:    //A
   BEGIN
      //按A列排序
   END;
   1:  //B
   BEGIN
    //按B列排序
   END;
   2: //c
   BEGIN

   END;
   3: //D
   BEGIN

   END;
   4:  //E
   BEGIN

   END;

 END;
end;

procedure TForm1.CornerButton1Click(Sender: TObject);
var
temprow :integer;
begin
     for temprow := 0 to stringgrid1.RowCount-1 do
     begin

       if stringgrid1.Cells [0,temprow].IsEmpty then
       begin

         break;     //此处不能用EXIT 哟
       end;

     end;
    addRow(temprow);

end;
procedure TForm1.CornerButton2Click(Sender: TObject);
var
 temprow:integer;
 val :array[0..4] of Variant;
begin
  if stringgrid1.Selected<>-1 then
    begin
     temprow:= stringgrid1.Selected;
     val[0]:='AA';
     val[1]:='BB';
     val[2]:='CC';
     val[3]:='DD';
     val[4]:='EE';
     insertRow(temprow,val);
    end
    else
    begin
      showmessage('你没有选择');
    end;

end;

procedure TForm1.CornerButton3Click(Sender: TObject);
var
col,temprow ,rowcount:integer;

begin
  if stringgrid1.Selected<>-1 then
  begin
   temprow:= stringgrid1.Selected;
   delRow(temprow);
  end
  else
  begin
      showmessage('你没有选择');
  end;
end;

procedure TForm1.DelClick(Sender: TObject);
var
col,temprow ,rowcount:integer;

begin
  if stringgrid1.Selected<>-1 then
  begin
   temprow:= stringgrid1.Selected;
   delRow(temprow);
  end;
end;

procedure TForm1.FormCreate(Sender: TObject);
var
col,row:integer;
begin
   row:=50;  //添加50行测试数据
   for row := 0 to (50-1)   do
     for col := 0 to stringgrid1.ColumnCount-1  do
      begin
       stringgrid1.Cells[col,row]:=row.ToString  ;
      end;
    stringgrid1.Options:=[TGridOption.RowSelect,TGridOption.Header,TGridOption.Editing,TGridOption.HeaderClick];  //允许选择整行，显示标题 ,单击，

   {
   property Options: TGridOptions read GetOptions write SetOptions stored OptionsStored;
   TGridOption = (AlternatingRowBackground, Editing, AlwaysShowEditor, ColumnResize, ColumnMove, ColLines, RowLines,
  RowSelect, AlwaysShowSelection, Tabs, Header, HeaderClick, CancelEditingByDefault, AutoDisplacement);
}
//以下是单元格的对齐方式 ，没有针对各列的对齐方式，如针对某列的对齐方式，则需要重绘
  stringgrid1.TextSettings.HorzAlign:=TTextAlign(0); ////文字横向对齐：0居中,1左,2右
  stringgrid1.TextSettings.VertAlign:=TTextAlign(0);//文字纵向对齐：0居中,1左,2右
  //以下加入样式
  form1.StyleBook :=StyleBook1;//样式 
  StyleBook1.Resource.LoadFromFile('style\GoldenGraphite.Style');

end;

procedure TForm1.InsertClick(Sender: TObject);
var
 temprow:integer;
 val :array[0..4] of Variant;
begin
  if stringgrid1.Selected<>-1 then
    begin
     temprow:= stringgrid1.Selected;
     val[0]:='AA';
     val[1]:='BB';
     val[2]:='CC';
     val[3]:='DD';
     val[4]:='EE';
     insertRow(temprow,val);
    end
    else
    begin
      showmessage('你没有选择');
    end;

end;

end.