Yes, you must choose a section, however, if there is more than one section within the course, enrolling a user in one section will allow them access to all sections of the course. It will cascade down.
The grace period is a defined amount of time after a quiz ends that students can review/change their responses and submit a quiz without flagging as late. The grace period must be larger or equal to 1 minute. There is no timer for the grace period displayed anywhere on an exam window for a student to view. There is a timer for the exam though displayed at the top of every exam page with a countdown
You will want to communicate with your students regarding the grace period as they may be confused after the timer runs out. During the grace periodthey canstill change their exam answers for at minimum 1 minute after the exam timer runs out. The grace period is to allow to hit “submit”. You cannot restrict students from making changes during the grace period. It is possible that students can change a few answers during the grace period and press submit all before the end of the grace period.