Query MongoDB collection and find rows from 7 days ago
I can't test this at the moment, but that's the basic format. You should change your date data type to ISO so it works easily with the below code:

var lastWeek = new Date();
lastWeek.setDate(lastWeek.getDate() -7);
db.messages.find({ "rep_header.share_date_2.$date": { $gte: lastWeek} } } );