Recently, I’ve try to upload a new module into our website, but after a fail “unable to install all the components”, we are now unable to manage the website cause all the Menu Type Item disappear — and by the same time, make the website down.
So where can I find the core “menu item type” to remplace and try make all this work fine.

Before you starting trying to edit Core Joomla files to try and fix things….dont! I have told many people that editing core Joomla files can results in security issues, prevent other functions from working, get overridden on a Joomla update and more.
What I would try first, it download a fresh copy of Joomla 2.5, and extract only the following folders:
Then, zip them up, upload via the FTP to the root folder and extract.