You should create arabic store view rather than store, if you want to share the information between the store views. If you wish to change the top links and static content magento provides translate inline tool. Go to
system->configuration->developer->translate inline
Enable for front end then go to frontend and you will see a book like icon click there and popup will come then translate the words, don't forget to select the store view.
If you wish to translate the category names you can do it in admin panel by selecting specific store view for category then uncheck use defeult value option and fill the translated text in the name :)