Cards that meet all of the conditions below and have unique card numbers can be placed in this card’s Digivolution cards with this card's [On Play] effect.-The cards must be in your hand or trash.-The cards must have [Cyborg] in their traits.-The cards must be red or black Digimon cards.-The cards must be level 5 Digimon cards.

Yes. The effect reads, “You may trash,” so you can choose not to trash any cards.

Yes, you can. For example, if your opponent activates an "if your opponent has as many or more total Digimon and Tamers as you, delete 1 of your opponent's highest level Digimon. Then, delete 1 of your opponent’s lowest level Digimon" effect, you can activate this card's "when [...] would be deleted" effect for the 1st deletion, then you can activate this card's "when [...] would be deleted" effect for the 2nd deletion that was activated by your opponent.