Try it. He moves the mouse to the screen (Win, iOs, Android). So you can use this to find when the cursor is out of your control. And for MouseDown, try using MouseDown on the form.
function MousePos: TPointF;
var
MouseService: IFMXMouseService;
begin
if TPlatformServices.Current.SupportsPlatformService(IFMXMouseService, IInterface(MouseService)) then
Exit(MouseService.GetMousePos);
Result := PointF(0, 0);
end;