Use Timer component and this code for onTimer event.

procedure TForm1.Timer1Timer(Sender: TObject);
begin
  Form1.Caption:=DateTimeToStr(Now);
end;

Try this algorithm:

var
  Year, Month, Day: Word;
...
procedure TForm1.Button1Click(Sender: TObject);
var
  YourDate, JunFirst: TDateTime;
  Week, More, Days: Integer;
  DaysLeft: Real;
begin
  YourDate:=StrToDate(Edit1.Text);
  DecodeDate(YourDate, Year, Month, Day);
  JunFirst:=EncodeDate(Year, 1, 1);
  case DayOfWeek(YourDate) of
    1   : More:=0;
    2..7: More:=1;
  end;
  Days:=Trunc(YourDate-JunFirst)+1;
  Week:=(Days div 7)+More;
  DaysLeft:=Days mod 7;
  case DayOfWeek(JunFirst) of
    1   : More:=1;
    2..7: More:=9-DayOfWeek(JunFirst);
  end;
  if (DaysLeft-More>=0) then Week:=Week+1;
  Label2.Caption:='Week number '+IntToStr(Week);
end;

You can use operation of a difference between dates. The answer is a count of days between them.

procedure TForm1.Button1Click(Sender: TObject);
begin
  Label3.Caption:=FloatToStr(
    StrToDate(Edit1.Text)-StrToDate(Edit2.Text))+
      ' days between of this dates';
end;

You may use DayOfWeek function. DayOfWeek returns the day of the week for a specified date..

procedure TForm1.Button1Click(Sender: TObject);
var
  MyDate: TDateTime;
begin
  MyDate:=StrToDateTime(Edit1.Text);
  case DayOfWeek(MyDate) of
    1: Label2.Caption:='Sanday';
    2: Label2.Caption:='Monday';
    3: Label2.Caption:='Tuesday';
    4: Label2.Caption:='Wednesday';
    5: Label2.Caption:='Thursday';
    6: Label2.Caption:='Friday';
    7: Label2.Caption:='Saturday';
  end;
end;