Can Spotlight be configured to search ALL files on the hard drive (or is there a powerful alternative) - like Windows' Start Menu search can be?
Solution 1:
I can recommend EasyFind and Find Any File (of which I'm the author, incidentally). Both search for file names on entire disks.
They search even in places where Spotlight never looks (e.g. in the System and Library folders).
In case of Find Any File, you can even easily search as root user, so that it even finds files usually not accessible to you. FAF also lets you save a set of preferred paths, either as a default or as a "search" document that you can open as a pre-configured search configuration.
Solution 2:
Unfortunately, no, you can't add custom paths to Spotlight.
I use and recommend Alfred, which lets you set a custom Search Scope:
You can search normally just by typing, or press space (which inserts a '
— the operator for a File Search) then type to search all paths: