For notification on not playback: that's just Idle. Idle is neither record nor play - so yes it would notify you if it stops recording if used barebones, but if that is an issue, you can just add an IF statement for IF it is recording - stop, then do the notification.
As for your programming, why bother having the IF/Else statement to stop? If it's not playing, a stop command simply won't do anything to begin with: you're just over complicating things there.
The not always disarming, and the programming not triggering when disarming from the panel are most likely not an issue with the mockupancy: it's likely an issue with the alarm panel or it's driver: networx however is so outdated at this point, that I doubt you'd be able to find much support except on here - provided someone here is familiar with the product.
I fear your best answer will be getting a current alarm panel to replace the networkx. GE/interlogix has been gone for nearly 5 years, with end of support nearing 3 years....