Multilingual homepage
No, you don't need to duplicate file, just go to /admin/config/regional/translate/translate and search for what you want to translate.

To be able to translate strings or variables from custom page.tpl.php file, all of them in the file need to be translatable, ie. to be in t() function, so if you can't find words that are from some custom .tpl.php file, make sure that particular string or variable in the file is translatable (in form like I mention).

For more information about using function t() look this.