can I manage menu too?

Thanks for your questions!

xili-language contains four ways to insert multi-language menu: template tags, widget and nav-menu based on xili-language-list function. The fourth way is php coding using other core functions of plugin.

Custom home page: you can built yourself your language menu

Thesis is not a free theme, I am not able to look functions.php file and verify if the authors meet the wp rules for localization. xili-language is free and donations are welcome

some links:

http://multilingual.wpmu.xilione.com/

https://dev.xiligroup.com/?p=1432