> Is it safe to PAUSE and then shutdown WinHTTrack, or
> do I need to keep the program open all the time?
If you Cancel a mirror, you can not resume. Cancel deletes everything in the
cache not already mirrored so Continue must redownloaded from that point on.

Mirror -> Pause/Mirror -> Resume is your friend.

Killing WinHttrack is the same as Cancel.  Just minimize it.