Generally, the more responsible jobs require Times reporting experience. Copy editing is treated as an important job and our opinions are given respect. There's a collegial relationship between the assigning editors, who make up the backfield, and the copy desk. The copy editors ask the reporters questions, but they also consult with the backfield on major changes. The editing process can involve many people at once.
Questions come from the news desk, or from other senior editors, or from the slot and the backfield.
And it's the copy editor's responsibility to get all the questions answered. No, there's a separate makeup department that handles layout. About 2 makeup editors are assigned to each desk on any given night. To other sections of the paper or into the backfield, generally. One often gets the satisfaction of working with the best reporters and editors and the feeling of having a serious responsibility at a great newspaper.