Ain - 500 Years In The Future (OP07)

Product Details:

Card No: OP07-002
Rarity: Rare
Color: Red
Card Type: Character
Cost: 7
Power: 6000
Counter: -
Attribute: Slash
Type: FILM/Neo Navy
Card Set: -500 Years in the Future- [OP-07]

Effect:
[On Play] Set the power of up to 1 of your opponent's Characters to 0 during this turn.

Card Questions/Ruling:

• If my Leader attacks my opponent's Character that has a power of 0 due to this Character's [On Play] effect, and my opponent uses [Counter +1000] on that Character, does that Character's power continue to be 0?
  No, the Character's power will be 1000 during the battle.
  
• During my turn, my opponent's "OP05- 012 Hack" with a base power of 5000 is given +2000 power by the [Counter] effect of "OP07-018 KEEP OUT", making its power 7000 until the end of my opponent's next turn. If I use this [On Play] effect of my Character on that "Hack" card, will that "Hack" card's power be 0 during my current turn, and then 7000 during my opponent's turn? "Hack" card, will that  Hack" card's power be 0 during my current turn, and then 7000 during my  opponent's turn? 
  Yes, in this case, it's power will become 7000.