Main language where the edits were made (global menu template was changed, Global fonts and color were change). It is fine on the this page. hidden link
Secondary language. Changes are not updated for other languages. hidden link
In the session I had changed the logo, which was automatically updated though,...
My question is: What is wrong with this plugin since I cant just update and how do I make it work for the future?
2) Could you please share your Debug information with me?
You can read a detailed explanation about it here. (http://wpml.org/faq/provide-debug-information-faster-support)
The debug info will give me a lot of information about how your site is configured.