1. If you need to make a scripted action while an AI is dead when the map started, for some unknown reason (maybe a bug) you cannot use the only condition Query if [HealthState] is [Equal to] [HealthState_Dead] on any linked objects(s) [MYSELF], the script won't work. In order to succeed in the operation you must add a logic OR operator in the way as it's shown in the picture:
TDS Triggerscript action when AI dead
Only in this precise order the script will work.