Since the previous topic http://community.norton.com/t5/Norton-Internet-Security-Norton/An-issue-with-Firefox/td-p/962351 is closed, I'd like to share the solution (i suppose - it is the solution), in case somebody experiences similar issues.
First, I want to apologize for being unjust to NIS: probably all the crashes didn't have anything to do wit it at all. The culprit was firefox's proxy settings. Previously (and it's a default option) proxy was set to automatic. When I changed it to no-proxy - all crashes stopped.