5 official rulings from Bandai, last ruled Mar 28, 2024. Straight answers to how this card actually resolves.

Does this card's "if this effect trashed a card with the [Seven Great Demon Lords]" refer to the card trashed from my hand or my opponent's level 6 or lower Digimon that I deleted?
It refers to the card trashed from your hand.
Ruled Mar 28, 2024
If an effect plays an opponent's Digimon while this card is in the battle area, do I have to activate <Delay>?
No, <Delay> effects are "trash this card in your battle area to activate" effects, therefore you can choose to not trash the card in order to prevent them from activating.
Ruled Mar 28, 2024
When an effect plays an opponent's Digimon into the breeding area, does this card's <Delay> activate?
No, it doesn't.
Ruled Mar 28, 2024
If my opponent uses [BT13-020]/[ShineGreymon: Burst Mode]'s effect to play [Marcus Damon] as a Digimon, does this card's <Delay> activate?
No, it doesn't. [Marcus Damon] is played as a Tamer by [BT13-020]/[ShineGreymon: Burst Mode] effect and then it's treated as being a Digimon by an effect, therefore it isn't considered to be played as a Digimon.
Ruled Mar 28, 2024
Does this card's <Delay> also activate when one of my effects plays an opponent's Digimon?
Yes, it activates.
Ruled Mar 28, 2024
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Questions and answers are Bandai's official rulings, collected and translated by the DigimonCardGame Wiki community and reused here under CC BY-SA. Card names and card text are © their respective publishers; Combalo is not affiliated with Bandai.