Can scheduled reports be automatically saved to a chosen directory after they launch on the scheduled date/time?
Yes. On the Destination tab of the Report Maintenance window, choose PDF for the Destination. Then specify the directory in the PDF/Export Default Filename.
If you also want to print the report, then you will need to set up two Report definitions for the report, one as described above, and one with Printer as the Destination.
Then, in the Actions of the Scheduled Launch Point, you need to launch both reports, or use the Launch All Reports action.