Of course (via csv). You can create multiple export formats with different subsets of entry data. More discussion tip and tricks on using the Dataform can be found in the Database activity forum.
Itamar Tzadok
Publicaciones hechas por por Itamar Tzadok
Make sure the Site administration -> advanced features with Enable completion tracking set to yes (as shown in the your attached screenshot) is saved. Then you should be able to see in the course settings a section titled Completion tracking (missing from your second screenshot). If you close and reopen and still don't see this section try refreshing caches.
By the :edit option of the entry author pattern. In 2.6 onward it's the pattern [[EAU:edit] ]. In earlier versions it's ##author:edit##. In browse mode it works like the :name pattern, that is, displays the entry author's name linked to the user profile. When a teacher edits the entry, the pattern displays a dropdown of the course participants and selecting a participant will set the entry userid to the user id of that participant.
Not possible in the standard module. Can added on with some development. The Dataform module has a similar feature which allows instructor to set the entry owner on behalf of students. What use cases do you have in mind? If a selected student is unenrolled, does the entry preseve the selection or reset it? etc.