1) are they unplayable due to the 'no power cards of x type' events?
2) are they affected by other things. EEs, or xbabies inherent?
It's a special first before it's a "power card" so they wouldn't be affected by those events. Likewise, if you have "No specials may be played this battle.", these cards wouldn't be playable because of the exact same reason.
QuoteMeta #84: Specials which indicate that they act as Power cards only act as Power cards in that they can sometimes be used to attack or defend (as specified on the Special). They do NOT take on any other properties of Power cards i.e., they count towards X-Babies K.O., they do NOT fuse with other MultiPower Power cards, they cannot be removed with an EE Special.