"They write us a book."
Translation:Ils nous écrivent un livre.
"on" is not an exact substitute for "nous", especially because it only exists as a subject.
As in the similar sentence in the singular that appeared earlier in the exercise the structure of the English sentence is poor. To a native speaker 'They write us a book' is not a well written sentence. For example, ' He writes them a letter' means 'he writes a letter to them'. What this exercise meant was 'They write a book for us' not ' to us'. In the construction 'writes us' a 'to' is implied but a 'for us' must be written explicitly.
Yes, if you mean to emphasize the fact that "they" are doing something different from what others are doing.