Example: Can I do an additional 10 damage with Shedinja DX, to the defending Pokemon, if I turn it into a {D} Pokemon with Weavile and use Darkrai Lv. X's Power to make every {D} energy attached to Shedinja DX +10?
No, damage modifiers only work when the attack itself does "base damage", meaning the number to the right of the attack name. If there is no number there, that damage cannot be modified, unless the attack text itself says "do x damage". Damage Counters are not base damage, it is an effect of an attack, and therefore, does not receive the bonus from damage modifiers.