>> "#1. What is the difference between the flags TA_USER and TA_SYSTEM ?"
This is described in TurboActivate.h. The difference (the only difference) is where the files are stored. With TA_SYSTEM they're stored on a system-level basis (and thus accessible by all users on the machine)
TA_USER the files are stored on a per-user basis (and thus not accessible by other users).
In either case the same activation "slot" or verified trial "slot" is used whether you're using TA_SYSTEM or TA_USER. Using TA_USER doesn't turn the node-locked licensing into per-user licensing.
So, if 2 users activate on the same computer activate on the same computer they'll use the same activation slot. Similarly if they use a verified trial as different users on the same computer the same verified trial will be used.
>> "- if unverified trial was used before, the verified trial takes it into account and continues with the remaining days (possibly being directly expired)"
Correct.
>> "- if verified trial was used before, the unverified trial seems to be directly expired (no continuous behavior like in the first case)Am I right ?"
Correct. There is an error that you can handle.
>> "With license, it's possible by reinvoking Activate(), but I don't see any way to do so with verified trials."
That's correct. We haven't seen a need for it. We'll implement it eventually. Not in 4.1, but later in a bugfix release in the 4.1 branch.