When the Alert Supression Field is true, it will Suppress all Alerts from Triggering
Alert 1 will not work because as long as a single Device with the Custom Property of "ImportedFromBigBrother" was No, then this Alert will never trigger.
Alert 2 is correctly designed. The Node will have to be down and "ImportedFromBigBrother" is yes and it will Alert.
Always use the Trigger\Reset Conditions Tabs to setup your Alerts.
Less than 2% of Customers' Alerts will use Alert Suppression. Alert Suppression was designed so if the Router of a Network was down, it would not Alert when the Devices were reporting as down.