If the circle is a stroke, you can create guides with the help of a centered rectangle and then use scissors tool to cut the portion:
If it's not a stroke, use multiple points for scissors and then remove the unwanted part using Direct Selection Tool. Then join the ends using Cntl+J and then round the corners.
In my opinion, all chapters should always start on the right side page ... all of them.
In your example, Pg3 would be blank, unless there were additional text/images from the previous chapter overflowed to it. Leaving blank left side pages (verso) is fine. However, you should ensure you don't leave blank right side pages (recto).
This eliminates most ...