Mozdev.org

All my accounts disappeared after I restart Firefox

WebMail Notifier utilizes Password Manager of Firefox. If you clear "Saved Passwords", WebMail Notifier accounts will be gone. Don't clear "Saved Passwords".
You can set this option here.

Tools -> Options -> Private Data -> Always clear my private data when I close Firefox

Uncheck this option.

I want to check all unread mails in Gmail(including mails that are not in inbox).

Type about:config in location bar.
Find wm-notifier.webmail4.inboxOnly and set it false