Too many questions for one posting ... but I'll give a partial stab at response.
1. Do all activities need to be converted? - depends upon changes to activities. In the case of assignments yes, they should be converted to the new.
2. If you still have both assignment versions available in the 2.6 and for some reason a restore of a course doesn't convert, then yes, use convert tool. Once done with restoring courses and converting assignments hide the old in System Admin. Teachers won't be able to use the old anymore. If you restore old courses, however, one might have to turn that on until the old course is restored. (not sure about that one).
3. user data won't come across.
4. reduction of courses ... there is an easy button in the 1.9 course ... re-set. That removes users from the course, their submitted assignments, .... all the student work. Basically sets the couse to be used by a new set of students. That might reduce the size of the backup depending. One would have to run a backup of the just re-set course to see if the backup file (the .zip) is smaller. Also remove any backups they might have stored - 1.9.x and less had an issue with including backups inside of backups. Note: they should download those backups before removing for archiving purposes.
Also, much depends upon how good teachers are with file management. Ask them to remove any file/files NOT linked in their courses.
Make sure you keep a backup/archive of all the course ID folders of the 1.9 data folder. Missing files could be made available to teachers via file system repo IF their old course ID folder is known and that ID folder is moved into a file system repo setup just for a single teachers new 2.x course.
'spirit of sharing', Ken