What role does the teacher play in the deductive presentation of grammar?

For better classroom management, what should the teacher do while the students are doing activities?

When a teacher intends to present or explain a new language point, which of the following group methods is mostly recommended?

_______terrorism, the world would be much more peaceful.

When a student has made a sentence “I borrowed a paper from Miss Li”, the teacher says “Do you mean a piece of paper?” Here the teacher is playing the role of a(n)______.