It refers to a card that contains the specified text or icon in its name, traits, effects, inherited effects, (Rule), digivolve requirements, DNA Digivolve, 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, you cannot.A Digimon that gains <Alliance> from this effect attacks if possible.

Yes, both have to be XX.For example, "1 level 4 or lower Digimon card with the [CS] trait or that is yellow or black" means either "1 level 4 or lower Digimon card with the [CS] trait" or "1 level 4 or lower Digimon card that is yellow or black." In both cases, the card must be level 4 or lower.

No, they are not immediately deleted at this point in time.All activated effects are resolved, after which a rule check occurs. At that point in time, all Digimon with 0 DP are deleted simultaneously.