Session management?

I have few question regarding session management:
I am running Tomcat with Eclipse plugin.

1- Is there a way to tell the container not to start a user session automatically?
When I call request.getSession(false) I always get a session??

2- When a user logout, I call session.invalidate() and forward to the login screen. If the user attempt to log in again, if I call session.isNew() it returns false.
Isn't suppose to return true, because the original session is invalidated, and a new session is created?

3- FireFox issue: After a user logout, if I hit the browser back button few times, the session is reconstructed with the session objects inside of it. It doesn't happen with IE.

What I am trying to do is simple. When the user logout, I want to make the user unable to go back and access any pages.

Thanks

See the bazillion topics that ask how to disable the back button. The all say the same thing:

1) disable caching on the pages
2) Employ the PRG pattern

With regards to sessions, I think you are over-thinking things. Let the container do as it will with sessions. It's almost always the right thing once you get the above set up.