If I use Exeggcute's "Propagation" Ability to retrieve it from the Discard Pile into my hand, then use something like Ultra Ball or Computer Search to discard Exeggcute, would I be able to use "Propagation" again to retrieve it from the Discard Pile?
Yes, whenever Exeggcute is in the Discard Pile, you may use Propagation during your turn as long as its Ability has not been disabled.
Source: Plasma Freeze FAQ (2013-05-16), TPCi Rules Team (2013-05-16)
If I use Weavile's "Vilify" attack to discard one or more Exeggcute, can I use Exeggcute's "Propagation" Ability to immediately retrieve it back into my hand?
No, you cannot. Propagation can only be used on your turn before your attack, not during your attack nor afterward.
Source: Plasma Freeze FAQ (2013-05-16), TPCi Rules Team (2013-05-16)
If I use Cofagrigus' "Six Feet Under" Ability and Cofagrigus is either my last Pokemon in play and/or is my opponent's last prize, but the three damage counters placed onto my opponent's Pokemon allow me to KO their last Pokemon and/or take my last prize, what happens next?
If both players arrived at a win condition at the same time but one player has more win conditions than the other (like KO'ing the last Pokemon AND taking their sixth prize), the player with the most win conditions met wins the game. However, if both players have the same number of win conditions, the game is declared a Draw and a one-prize Sudden Death game takes place to determine the winner.
Source: Plasma Freeze FAQ (2013-05-16), TPCi Rules Team (2013-05-16)
If I have two Clefables in play, can I use "Moon Guidance" twice on the same Pokemon assuming I flip heads for both?
Yes, you can.
Source: TPCi Rules Team (2013-02-28)
If my Lugia EX knocks out an opponent's Garbodor with the "Garbotoxin" Ability and a tool attached, does Lugia EX's "Overflow" Ability turn on in time for it to take two prizes?
Nope, Garbotoxin is still active when Garbodor is KO'd, so Lugia EX does not get to take 1 more prize card for Overflow.
Source: TPCi Rules Team (2013-02-28)
If I have two Magnezones in play with the "Dual Brains" Ability, does that mean I can play 4 Supporters during my turn?
No, you cannot. Dual Brains says you may play 2 Supporters, period; it doesn't say "an extra supporter" for each Magnezone.
Source: Plasma Storm FAQ (2013-02-07), TPCi Rules Team (2013-02-07)
When Braviary uses its "Big Wing" Ability, who chooses which of the opponent's Benched Pokemon get brought forward?
The ability says "have your opponent switch..." so the opponent gets to choose.
Source: Plasma Storm FAQ (2013-02-07), TPCi Rules Team (2013-02-07)
If my Active Pokemon is Snorlax with the "Block" Ability, what happens to my opponent's Active Pokemon if I play Escape Rope?
Escape Rope causes the Pokemon to switch, but Block only prevents Retreating. The opponent switches their Active Pokemon when Escape Rope is played.
Source: Plasma Storm FAQ (2013-02-07), TPCi Rules Team (2013-02-07)
If my opponent's Active Pokemon is Snorlax with the "Block" Ability, what happens to my Active Pokemon if I play Scramble Switch?
Scramble Switch causes your Pokemon to switch, but Block only prevents Retreating. You can switch your Active Pokemon when Scramble Switch is played.
Source: Plasma Storm FAQ (2013-02-07), TPCi Rules Team (2013-02-07)
If my Active Pokemon is Togekiss with the "Bright Veil" Ability, do I bring up one of my benched Pokemon when my opponent plays an Escape Rope?
No. Bright Veil prevents your part of the "Each player switches his or her Active Pokemon" part of Escape Rope, so your Active Pokemon stays put and you can't bring up a benched Pokemon. However, your opponent does switch.
Source: Plasma Storm FAQ (2013-02-07), TPCi Rules Team (2013-02-07)