The direct answers to your questions are
1. Monitor status change will be immediately reflected on Home/Monitors. Not on Home/Monitor Groups.
2. Down monitors will not be moved to top. Down monitor count at the top will change. You can filter by clicking the count.
It is not a full refresh of the page/data on regular interval. Only when there is a change in status for any monitor, that change alone will be pushed to the client and reflected in the icon next to the monitor name and status count. The monitor row itself will not be moved to top.
When there is no change in the status for all monitors for a long time, nothing on the page will be changed. This behaviour is causing the doubt on refresh, I understand. We will change this behaviour to full data refresh on regular interval. I will update this post once the change went live.