There shouldn't be a Safari icon on your Deskop. Only your Dock.
And try installing Safari from here > Safari 5.1.7
Safari is a pre installed native Mac OS X application. No need to purchase anything.
First, delete all copies of Safari (and any other built-in applications) other than the one in the Applications folder. Never move or copy those applications.
Then rebuild the LaunchServices database. If you have one of the so-called "utilities" that does that, you can use it. Otherwise, proceed as below.
Back up all data if you haven’t already done so. Before proceeding, you must be sure you can restore your system to the state it’s in now.
Launch the Terminal application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ If you’re running OS X 10.7 or later, open LaunchPad. Click Utilities, then Terminal in the page that opens.
Drag or copy — do not type — the following line into the Terminal window, then press return:
/System/Library/Frameworks/CoreServices.framework/Versions/A/Frameworks/LaunchServices.framework/Versions/A/Support/lsregister -kill -r -domain user
Log out and log back in.