1. If you want to get data on the previous week, then you can schedule this report on Sunday and get data for the entire week. The same refers to current month parameter, you can generate it at the last day of the month and then get all data you need. Thanks for the feedback on the sorting and tape jobs, I will pass this info to the dev team.
2. This report shows only current information you have in the catalog. If I got you right, you would like to do historical reporting on the tape jobs?