I've read a lot of questions about that but I want to be sure.
I have two windows (of IE), with the first window I'm making a search on a screen and then, I'm making another search with the second window. After that, I'm losing one of my two sessions and here my question, is it possible to have 2 windows that make a different search and which have their own results in their own sessions or is it impossible ?
All IE windows and tabs are going to be sharing the same session. If you also have Chrome and/or Firefox, each of those browsers will have their own sessions, but the sessions for all of the windows and tabs for a Firefox will likewise all be the same session, as is true of almost every other browser. In other words, the sessions are unique per-browser program, but not within the browser program.
JSF is not particularly good at working with multiple browser windows/tabs, however. As far as it goes, I don't have a lot of love for them as a user, either. I have the browser set to open tabs, not windows, so "pop-ups" don't pop up. Largely because at any given time, I'm already hip deep in application windows, so multiple windows per app is more than I need.
An IDE is no substitute for an Intelligent Developer.