Can I use Professor Elm's Training Method if there are zero cards left in my deck?
No, you cannot search through your deck if there's nothing there to search. If there are cards in the deck you can fail to find a Pokemon because you don't know what may be in a deck, but since you do know whether there are ANY cards or not you cannot search through an empty deck.
Source: PUI Rules Team (2011-09-22)
If "Raikou & Suicune LEGEND" attacks "Suicune & Entei LEGEND", how is weakness calculated?
Since "Suicune & Entei LEGEND" is weak to both of "Raikou & Suicune LEGEND's" types (Electric and Water), you would multiply the damage x4.
Source: Unleashed FAQ (2010-05-13), PUI Rules Team (2010-05-13)
Do the LEGEND cards with two Pokemon on them (i.e. "Entei & Raikou LEGEND", etc.) count as two Pokemon while in play?
No, they only count as a single Pokemon when in play, even if your opponent takes 2 Prize cards when they are knocked out.
Source: Unleashed FAQ (2010-05-13), PUI Rules Team (2010-05-13)
Can I use Mew's "Re-creation" attack to choose a Lugia LEGEND card with the attack "Elemental Blast" written on it from my opponent's discard pile, and use that attack?
No, you can't use any attacks from a Pokemon LEGEND unless both pieces are in play.
Source: PUI Rules Team (2010-02-18)
If Primeape's "Top Drop" attack reveals a LEGEND Pokemon card with no HP printed on it, how much damage does it do (if any)?
No damage is done regardless of which LEGEND half is revealed by Top Drop, because even the half with HP written on it is not considered "a Pokemon" while in the Discard Pile.
Source: PUI Rules Team (2010-02-04), PUI Rules Team (2010-02-18)
Can I use Mantine's "Group Swim" attack to put one half of a Lugia LEGEND card in my hand?
Yes. Either half of the Lugia LEGEND card is still considered "a Water-type Pokemon", so you can search for it with Group Swim.
Source: HeartGold & SoulSilver FAQ (2010-02-11), PUI Rules Team (2010-02-11)
Can I play a Pokemon LEGEND as my Active Pokemon or on my Bench during setup?
No. Since a Pokemon LEGEND is not a Basic Pokemon you cannot play it during setup, even if you have both halves.
Source: HeartGold & SoulSilver FAQ (2010-02-11), PUI Rules Team (2010-02-11)
What if during setup the only Pokemon cards in my hand are Pokemon LEGEND halves?
Since you have no Basic Pokemon to place Active you will let your opponent look at your hand, then shuffle and redraw your hand as described in the rulebook.
Source: HeartGold & SoulSilver FAQ (2010-02-11), PUI Rules Team (2010-02-11)