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Confirmed - the JDK and Eclipse will work on Windows 8. I'm running Windows 8 RTM (64-bit). I just downloaded Eclipse from http://eclipse.org/downloads/packages/eclipse-ide-java-ee-developers/junor and the JDK from http://www.oracle.com/technetwork/java/javase/downloads/jdk-6u31-download-1501634.html. I'm not a Java developer, but I was able to open Eclipse and build and run a simple Hello World app.
Running Java in Windows 8 shall probably not be a problem, because Java is a portable and cross-platform language. Dependency issues are not non-existent, but they are minimized and isolated (if they exist) at a (usually low) layer of the code, and hidden from the user / API client. So if your code has a portability issue it will generally be an issue and not Windows 8-specific. (e.g. if your code breaks ported from Win8 to another OS, it is not Win8's fault)
So generally if java and javac run in Windows 8, all Java programs shall run in Windows 8 as far as no dependency issues arise. Installing in a partition as pointed out or running on a virtual machine Windows 8 can be a way to confirm yourself how much is possible to accomplish in this environment.
I would suggest checking out some of the other sites of the network, namely superuser may have an answer...
First, check you eclipse.ini (even a space at the end of a line can prevent eclipse from starting)
Second I am surprised to see java* file in your Eclipse distribution.
You shouldn't' have those, and instead refer to the right java (64 bits) in your eclipse.ini.
In both case, see this eclipse.ini as a good example.
Check also the <workspace>/.metadata/.log (error log file).
I just added it there because it was asking for it, supposedly the best way it to put it in the PATH.
If eclipse is "asking for it", that means your current java installation is not part of the PATH. It need to be reference from the eclipse.ini file.
See also FAQ How do I run Eclipse?
In any event, don't copy any java files around.
Used in your eclipse.ini a path like:
-vm
C:/Prog/Java/jdk1.6.0_21/jre/bin/server/jvm.dll
Do you have the 64-bit version of Java? http://www.java.com/en/download/faq/java_win64bit.xml