It doesn't matter I think. Mine is only on when I need it. I turn it off when I don't have a use for it. Saves power But, as said, I see no problems leaving the unit always on. The drive has power but as it's not being used, there is no reason why it should wear out faster. There is a fan in the case though that might brake down sooner when the unit is always on but changes are the fan will work for years so this is not an issue.
By leaving it open I hope you mean leaving the power on? It's never a good idea to leave an optical drive's tray open because of dust collecting. But, you probably already knew this!