Do the individual pieces of LEGEND Pokemon count toward the 6 Pokemon needed for a player to declare themselves a winner when "Lost World" is in play?
Yes, each LEGEND Pokemon card counts as one Pokemon toward the requirement.
Source: Call of Legends FAQ (2011-02-10), PUI Rules Team (2011-02-10)
If a Stage 2 Pokemon or Leveled Up Pokemon is put in the Lost Zone, does that count as one Pokemon towards the 6 Pokemon needed for a player to declare themselves a winner when "Lost World" is in play?
No. Each Pokemon card counts toward the 6, including Basic, Stage 1, Stage 2, and Level Up Pokemon cards.
Source: Call of Legends FAQ (2011-02-10), PUI Rules Team (2011-02-10)
If an Unown-Q is put into the Lost Zone while it is attached to a Pokemon as a Tool, would it count toward the 6 Pokemon needed for a player to declare themselves a winner when "Lost World" is in play?
Yes. Once it is no longer in play, it reverts to being a Pokemon card again.
Source: Call of Legends FAQ (2011-02-10), PUI Rules Team (2011-02-10)
If my opponent has 6 or more Pokemon cards in his or her Lost Zone after my Pokemon uses its attack, but prior to the start of my opponent's turn, can I declare myself the winner with the effect of the "Lost World" Stadium?
No, you can't. You can only declare victory with the effect of Lost World prior to your Pokemon using an attack. Once you begin your attack, you cannot use Lost World's effect.
Source: Call of Legends FAQ (2011-02-10), PUI Rules Team (2011-02-10)
Let's say I have no cards left in my deck when my opponent's turn ends, the "Lost World" Stadium is in play and my opponent has 6 Pokemon cards in the Lost Zone. Can I declare myself the winner at the beginning of my turn, before drawing a card from my deck?
No you can't. You can only declare yourself the winner with the effect of Lost World during your turn, but since you can't draw a card from your Deck you cannot start your turn, and therefore you lose.
Source: Call of Legends FAQ (2011-02-10), PUI Rules Team (2011-02-10)