If the Quicklaunch toolbar isn't showing right click a clear area on the Taskbar and uncheck Lock the Taskbar. The right click it again and choose Toolbars\Quicklaunch. Drag the vertical spacer a bit to the right to make room and then just drag any shortcut you want.
As for the icon on the right, you must have plugged something in to a USB port such as card reader or removeable drive. Before you remove such device you should click this icon, choose the item you wish to remove and then click on Stop. You will get a message that the hardware can be safely removed. If you have just unplugged something without going through thus procedure it may hace become confused. Plug it in again and then remove it correctly.