Sorry, the weekday selection does not affect "Run Upon Logout and Shutdown". Maybe in a future version.
Is there a way to delete (for example 1 month) old backups?
A specified number of older versions can be kept on a file-by-file basis using the Versioning settings. Then there is only one backup location containing multiple versions of each file. The files can be copied 1:1 or zipped individually (not ZIP Packages).
If you store your backups different, for example complete copies in separate folders, or using ZIP Packages, then
there is no built-in way and I would really recommend doing this manually. What if for some reason newer backups are not created but he old ones are deleted? And even if automated, how could the software be sure that the old backups don't contain anything that's missing from the new ones? This is all too dangerous, so there is no checkbox for that. Backups are meant to be kept forever in my opinion.