Moodle wil certainly meet all those requirements except the last two may be somewhat problematic. For the first six of these issues the basic setup of Moodle will easily cover them, that is, dependent on how you set the Moodle up. The 7th and 8th points require a little different approach, but well within the capabilities of Moodle Roles. However, the last point always going to be a stick in the mud.
What you need to find out is what format the software saves things into. What database did it use, if it used a database at all? How did it structure and backup course materials and so on. This does not mean that anything you might try is impossible, just some formats are easy to convert, some are not. Some of the materials you might be able to export as text and place them into Moodle easily. Some you might be able to convert from the database into a csv file edit the file a little and upload it directly into Moodle with little difficulty, but not necessarily easily. Some materials you may have to spend time reveloping and uploading to Moodle. The bottom line is, of course, the format the materials are presented in.