i dont think you need to install java to run the ide - it comes with a compatible version of the Java Runtime. You need to install java if you want to work on java projects.
Depends on the platform. "What do I need to start with CLion?" lists "Installed Java is required, Apple JDK 1.6.0_65+ is recommended" for OSX and "Oracle JDK/OpenJDK 1.7.0_51 is required" for Linux.
Only Windows bundles its own JVM, same as other non-IJ IDEs.
Yep, I had to install OpenJDK. Haven't tried installing on anything other than Linux, though.