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.

You can give that effect to such Digimon, but if the Digimon isn't affected by effects upon the trigger timing, the gained effect won't trigger.

No, you can't. A "by" condition can't be met if only some of the required actions are performed. In order for the conditions of this card's [On Play] [When Digivolving] effect to be met, you must place 2 of the specified cards from your trash as this Digimon's bottom digivolution cards.