Will zulu update packages properly update standard openjdk version 6 or should I do a installation from scratch? Also, do I need to do a root install or can zulu-openjdk install on individual users?
1) The current version of Zulu/OpenJDK is Java 8. Java 8 will be considered a different software from Java 6 and therefore will NOT update it. Rather you should install them side by side and then (optionally) remove Java 6.
2) You should be able to install Java as a normal user. At least if you use the “zip” or “gz” packages. Just unzip and run /bin/java.