In PHPStorm (IntelliJ spin-off) I can just do "Open Directory", and it will parse all the source files inside that directory into a new project automatically (if none exists yet for that folder). All those intelligent features you describe work right away.
You can. For java if you have a source directory, you New Project -> Java -> Create from existing source code. If there isn't an option for that in php, its because no body has written it, not because its not possible.
Why can't eclipse do that?