If you don't have Java 6 installed on your system (10.7/10.8), you can get it by simply typing "java -version" on the command line (terminal).
This calls the software update which gets Java 6 from Apple and it will be installed.
Some people got the Java 6 JDK from Apple Developer site or Oracle installed on 10.7/10.8
Hope that helps
The password for the administrator's account on the Mac. You can't install any software on a Mac without authorizing it with the Admin password.
BTW, this is not a downgrade, both 6 and 7 will reside independently on the Mac.