If you have a microflow as the datasource of the listview¸ then you can limit the retrieve to 7 records and sort it by date descending.
Your second option “How can I show all objects where the date is equal to the latest date found in the list view?”
If it is ok to do this via microflow: first get LatestDate by doing a retrieve with Range “First” and Sort by date descending. Then do a retrieve with XPath constraint “[Date = $LatestDate]”.