Regarding running program when Windows starts and running every monday etc... you can do it even now.
Go to the sticky note's reminder window and select the Repeat option. Also, click on the "Advanced" button to launch any program. You can configure it in the same window. See below:
Also, if you set the time to "mid night" time when the PC is off, the reminder will be executed when you switch on the PC and launch the program you have configured.
To automatically launch the program make sure that "Show reminder message" check box is unchecked (above window).