The healing and damage IDs are specific to the player (or Global entity) that is executing the command, so it needs to be the same player (or Global entity) that stops the DOT or HOT. If this is the case, yet your stop action still isn’t working, share a code of your script and we can investigate.
Actually, I did find a bug with Last Heal/Damage Over Time. I’ve fixed it internally, and the fix will be available for you Friday-ish. Thanks for bringing it to my attention!
Regarding the variable before the game starts, the earliest chance you have to execute something is with the “Ongoing - Global” Event. Just set your variable as the first action. If you do this in the top rule, it’s guaranteed to execute before any other rule.
Regarding projectiles, there’s a lot more that we’d like to do with them, but for now, there isn’t a way to do what you’re asking, unfortunately.
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