Ok, I played around for a while and I think I have the solution now! I hope...at least for me know works perfectly.
After (a lot) of tests I believe the issue is not in iTunes U, the course, the pdf or other... the only issue is about IOS version!
I made tests on my iPad 4 gen. but a lot of function were buggy. My iPad had iOS 8.2 and last version iTunes U (3.0)
Here what I did:
1) I've uninstalled iTunes U
2) I've upgraded iOS to iOS 8.4
3) I've reinstalled iTunes U app
Now ALL works very well!!! "Hand-in" homework is fantastic and works great, and now also "Private messages" (inside assignment) works! Also "grade" works perfectly.
The only thing still doesn't work is notifications about new messages (you need to check inside the course and inside discussion message (for general messages) or inside the assignment (for private messages), and this is very very annoying.... I hope Apple guys will fix that.