How do I (optimally) connect Elk-924 (high sensitivity relay board ) to DSC PGM output (sinks to ground)
If you want a common ground, you have to connect one.  You should be able to power the Elk from the external supply, as long as you also have a connection from the Elk's NEG to the DSC's AUX- or one of its COM terminals.  Don't connect both positive supplies to the Elk, just their grounds.

If you have trouble making that work, then you can look at an optoisolator.  If you intend to keep the Elk, any opto that can handle the trigger current will do (note the 1.2 mA is a minimum).