Parmanantly setting to Private browsing.
When you open "option" page and change your browsing setting to "always private browsing," you'll no longer see the "Private browsing" sign on the top corner of your website. Is this normal? When you set to use private setting temporarily, you will see "private browsing" sign on the top corner of website, so I am worried.
Opaite Mbohovái (2)
Yes, this is normal behavior.
https://support.mozilla.com/en-US/kb/Options+window+-+Privacy+panel#Never_remember_history
See also Private Browsing - Use Firefox without saving history
Your above posted system details show outdated plugin(s) with known security and stability risks.
- Java Plug-in 1.6.0_13 for Netscape Navigator (DLL Helper)
Update the Java plugin to the latest version.
- http://java.sun.com/javase/downloads/index.jsp (Java Platform: Download JRE)