You have to make sure that the Windows Installer components are in the
iamge. Then either install the JRE during FBA or post-FBA. There is no way
to create a component for the JRE since it ties into the security of
Windows.
Maybe. I never tried that component myself so can't speak for it.
I did however install Sun JVM (some older version) manually on some component-rich images of mine so theoretically it should work.
Perhaps that component is indeed missing something.
After all I prefer MS JVM that I componentized years ago