There is no such thing as "safari player", so I'm not sure what you are talking about. Perhaps playing a flash video that is on the web in the Safari browser?
Don't know what restarting the computer has to do with it either.
Therefore, I am not really sure what you are calling the "status bar". If you are talking about the status bar that would be located at the bottom of a Safari window, then while you have Safari open, head for View on the menu bar and select Hide Status bar (or you can use the "command" and "/" key combo to display and hide the status bar). If you quit Safari normally, it will maintain that selection the next time it is launched.
(Deleted duplicate thread - only one thread per topic is needed.)