1. This sort of thing is currently being specified for implementation in Moodle 2.0 Development:Progress_tracking. I have not read that in detail yet, so I don't know if it meets your particular requirements. (Now would be a good time to speak up if not.) -
Please don't ask when Moodle 2.0 will be finished If you want to start now, assume you will be using 1.9 and will have to upgrade later. Therefore, the answer for this is that currently Moodle only has limited facilities for tracking this sort of information. You will probably have to think about doing it outside Moodle for a while. You can export the gradebook from each course as a spreadsheet (or XML, or ...) to get the raw data to work with.
3. Courses can be categorised into hierarchical categories.
4. For students mostly pretty easy to use. Most of the bits of the interface that we know are tricky, and we really need to improve when we get time, affect teachers setting up courses, and even so it is not really difficult to use, it is just that some of the pages of options are a bit daunting because there are a lot of options you can control.
5. Yes. The words you need to search for in the documentation are 'Authentication' and 'Enrolment' plugins / methods.