Re: Sensei role!
When a teacher is asking you to do Kata, you do the Kata!
Most technique practice is Kata, there are many variations for each technique, yet at a particular time, the whole group is working on one of those, as the teacher directs. If the teacher directed you to a certain variation you should work on it, just like you would have performed a specific Kata had he instructed you to.
A good teacher will define some points in time to let you perfect the techniques and variations you desire. Those should not come instead of the grouped practice.
The teacher selection should be directed by multiple factors, including the group participants (for example - no point in letting 3/4 of the group who are having their second lesson, try to select a technique while a veteran group should allocate more time for individual techniques improvement and Randori). A teacher may also pick on a technique \ variation he feels the group is performing poorly or would assist in making people more aware of some principle they seem to neglect (the latter is more suited to an advanced group).
I don't think one should confront the teacher during class (if this is your implication), but talking with him politely after class and asking for explanations is legitimate (at least with my Sensei).