It refers to a card that contains the specified text or icon in its name, traits, effects, inherited effects, (Rule), digivolution requirements, DNA digivolution, DigiXros requirements, burst digivolve, App Fusion, Link, or Assembly requirements. For example, a card with [Knightmon] in its text would include cards with the name [DarkKnightmon] and cards with the text [Knightmon] in their effects.

No, it isn't deleted yet. Once all of the processing for the activated effect has resolved, a rule check will occur, then all of the Digimon with 0 DP are deleted at the same time.

Yes, both have to be on XX. For example, if text reads "level 4 or lower Digimon card with the [CS] trait or is yellow or black," it refers to a level 4 or lower Digimon card that has the [CS] trait or a level 4 or lower Digimon card that is yellow or black.