Also, I'm Un-Inebriatable: Deadpool ignores Poison and can't be the target of Mind Control or Penetrating/Psychic Blast.

New Writer: At the beginning of the game, choose one: Deadpool can use Ranged Combat Expert and Combat Reflexes or Deadpool can use Close Combat Expert and Energy Shield/Deflection. He can use those powers as long as he can use this special power.

If I have a character with more than one , can I uses Penetrating/Psychic Blast to target Deadpool and another character and then just not deal penetrating damage to Deadpool?
No. If you want to use P/PB, you can't target Deadpool.

If I have a character that can use Mastermind, and he is hit with Penetrating/Psychic Blast, can I transfer the damage to Deadpool?
Assuming the Mastermind character is expensive enough (he would have to be at least 141 points, normally, to transfer damage to Deadpool), sure.

Mastermind specifically states that the damage transfered is not an attack, so Deadpool is never actually targeted with P/PB in this case. Damage can transfer normally. Also, since Mastermind also specifically states that the nature of the damage (AKA: the fact that it is penetrating) doesn't change, Deadpool also can't reduce any of this transfered damage.

If Deadpool is damaged off of New Writer and is later healed back on this power, can he choose again?
No. The choice is made once at the beginning of the game and that is it. He can certainly still use the powers he chose at the beginning of the game, nothing would prevent that, but he can't choose all over again.