Menu items not translated when in blocks

Problems: some menus title strings are duplicated; in menu the "Home" item is not translated, the other ones are translated in Menu links but not in menus appearing in blocks, except if the node itself is translated.

What I did:
I installed from scratch Drupal 7.0 in English, Internationalization module 7.x-1.0-beta-3 from scratch and Variable module 7.x-1.0-beta2.
I didn't change the default theme.
I enabled the all parts of the module except "Multilingual forum" and "Taxonomy translation".
I added French and Mongolian as additional languages; as detection methods I chose first the browser, secondly the default (English). I created nodes in English, enable multilingual support for some of them, specially "article", translated one article into French and Mongolian, put links to these nodes into the main menu, displayed the main menu in a block, and the User menu in another block.
I installed the interface localization into Mongolian. I then translated a few strings of the "Menu" group of strings into French and Mongolian, specially my menu items names. "Home" doesn't appear in the "Menu" group of strings, but does appear in the "Buit-in interface" group, were it was already translated into Mongolian. In Home » Administration » Configuration » Regional and language » Translate interface, I updated the translations.

Then I updated the Internationalization module to version 7.x-1.x-dev.
I get an issue similar to http://drupal.org/node/1070690 which "is not a bug":
« PDOException: SQLSTATE[23000]: Integrity constraint violation: 1052 Column 'changed' in order clause is ambiguous: SELECT n.nid AS nid FROM {node} n LEFT OUTER JOIN {node} i18n ON n.tnid > 0 AND n.tnid = i18n.tnid AND i18n.language = :lang WHERE (n.language=:lang OR (n.language=:default_lang AND i18n.nid IS NULL)) ORDER BY changed DESC LIMIT 10 OFFSET 0; Array ( [:lang] => mn [:default_lang] => en ) in node_get_recent() (line 2196 of /var/www/drupal-7.0/modules/node/node.module).»
(I don't know what I should do for this, but it may play a role in the main symptom.)

When I went to my site, the main links were and are translated according to my browser language, except "Home" which is not translated (though the translation for the string "Home" exists). In the menu in blocks, only the translated node's name was translated, the other were still in English.
The menu titles: "Main menu" and "User menu" were not translated, though I had translated these strings of the "Menu" group. I discovered that identical strings are in the "Built-in interface" group and, if I translate them there, the menu titles get translated in the blocks, but this is not intuitive. Are these duplicate translations really necessary? If there are, at least the translator should be warned.

Now, in the main links, I have "Бидний тухай", "Home", "Өгүүллийн жишээ", "асуулга" and, in the Main menu inside a block, I have "About us", "Home", "Өгүүллийн жишээ", "poll", which mean the same things and point to the same nodes. But it's not very coherent, and I'd like "Home" to be translated.

This also means that there are at least 3 sources of translations for the menus: the node translation, the "Menu" group of strings, the "Built-in interface" group of strings. This is possibly necessary, but difficult to manage, and the translator is unaware of these subtleties.