How to use translations within a single node?

Hi. I've installed i18n project on my Drupal 7 and I've already enabled it and configured publish settings in my content type (Basic page).

So I have the ability to translate the page but once I do that another node is created and so the links are different. The main problem here is that If I set an option to add node to menu then two menu items will appear. And if I unset menu option in the translated node then the menu item will remain untranslated.

I've heard it is possible to translate single fields. So is it? And how do I configure it? If not then how would I add correct title for both languages for the menu? Note that I would like to have a single item in the menu and the item should point to a correct version depending on a user language.