In a game that goes to time and is tied, if I add prizes to my opponent's field with Palkia & Dialga LEGEND's "Time Control" attack on my next turn, do I win?
Yes. After regulation time (plus any additional turns) is completed, once you have fewer prizes remaining than your opponent, you win.
Source:
Triumphant FAQ (2010-11-04), PUI Rules Team (2010-11-04)
If the opponent has already drawn 2 prizes in the game, and then I use Dialga & Palkia LEGEND's "Time Control" attack to add two more prizes, how much damage would my Mismagius [GL]'s "Grudge" attack do on the following turn?
Even though the Time Control attack added two prizes to your opponent's pile, they have still taken two prizes during the game. So Grudge would do 20 damage plus 10 more for each of the prize cards they have already taken.
Source:
Triumphant FAQ (2010-11-04), PUI Rules Team (2010-11-04)
In a Sudden Death game, if I add prizes to my opponent's field with Palkia & Dialga LEGEND's "Time Control" attack, is the game won by the next player to take a prize, or the first player to take their last prize?
A Sudden Death match is complete when a player has taken all of their prizes, regardless of whether there is more than one or not. So adding prizes in this scenario makes it more difficult for the opponent to win.
Source:
Triumphant FAQ (2010-11-04), PUI Rules Team (2010-11-04)
When using Darkrai & Cresselia LEGEND's "Moon's Invite" attack, can you move damage counters to/from more than one Pokemon?
Yes. Basically the attack let's you rearrange your opponent's damage counters any way you want, as long as other effects, Poke-POWERs, Poke-BODYs, etc. will allow.
Source:
Triumphant FAQ (2010-11-04), PUI Rules Team (2010-11-04)