If I intend to use a Poke-POWER [or Ability], do I have to announce its name or can I just take the action specified?
You have to clearly communicate your intent to use a Poke-POWER [or Ability] by some method other than just performing its game effect. Show or tell your opponent which Pokémon is going to use what Power.
Source: PUI Rules Team (2008-11-13)
If I have 2 of the same Pokémon in play that have a Pokémon Power [or Ability], can I use that power twice? What powers wouldn't be useable twice, or more for that matter?
Sure, depends on the particular power though. If you had two Muks for example, then only one power is necessary.
Source: WotC Chat (2000-05-11)