Sorry I disagree-
I've never had any reason to use an oscilloscope on an intruder alarm nor do I need a £500+ multi meter (it would only get lost or broken out in alarm land)
Aged 17 or so I knew something like a 9600 required a power supply to run all 16 zones & multiple keypads & speakers
Who would have guessed more than 30 years later I'd still be having conversations with people who don't understand the basics principles,
Suitable current in day & alarm, suitable voltage at each device when running off the battery, if you've not got this you'll have problems
Your alarm appear to have lots of problems I've got lots of alarms with very few problems, its funny old world isn't it ?