If no Digimon was deleted by this effect” refers to a state in which, when resolving this Digimon’s [When Digivolving] effect, your opponent doesn't have a Digimon in play, or you try to delete an opponent's Digimon that can't be deleted with the effect. Essentially, if you didn't delete a Digimon with the effect “Delete 1 of your opponent’s Digimon with the lowest DP,” follow the instructions listed after “If no Digimon was deleted by this effect...

No. This effect reads, “Delete,” not “You may delete,” so if there’s a valid target in play, you must choose it with the effect. You can't choose to NOT activate the effect.

Yes. When there are multiple Digimon tied for lowest DP, you can choose any of them. This means you can choose the Digimon with the effect preventing deletion to get the “if no Digimon was deleted by this effect” part of the effect.

No. This effect specifies a card name, so you must have a card whose name is either [Gallantmon] or [X Antibody] in this Digimon’s digivolution cards. Having a card with [X Antibody] in its traits doesn't count.