There are many variables in the assignment dialogue, which makes it a challenge to find out what works for you.
As far as showing 'inactive' ones: team are alerted to that, and working on it.
As for a name displayed without dates: only dates are displayed for assignments that have been selected in the top icons (so if you unselect 'non-student parts' and 'other parts') the following may happen. The name of an elder shows up (because he is probably technically eligible for Bible Reading). But since his last 3 assignments may have been (probably have been) 'non-student' and 'other' parts only, the dates won't be shown, since you didn't 'ask' those.
Also if in the bottom part the 3 vertical dots, you select Assignment, rather than Meeting Part or Theme, it is easier to see of someone was an assistant.
Incidentally in a demonstration there is an indirect way of knowing: the student is listed first, the assistant second. So if you see
John Doe | checkbox, the person was assistant to JD
but if you see
checkbox | John Doe, the person was the student with JD as assistant.