No, you can't. A "by" condition can't be met if only some of the required actions are performed. The conditions for this [All Turns] effect require you to trash the specified number of digivolution cards.

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

Yes, it's deleted. After giving "[End of Your Turn] Delete 1 of your Digimon" to an opponent's Digimon, it activates as your opponent's own effect.

No, you can't activate it. When a card with an effect that's pending activation leaves its current area while activation is pending, the effect can no longer be activated. In this case, being trashed from digivolution cards will trigger EX10-044 [Damemon]'s inherited effect, but it leaves the trash before activation, therefore it doesn't activate.