If my opponent mulligans several times during setup, may I choose to take 1 card from the top of my deck, look at it, and then decide whether to continue drawing my next mulligan?
When drawing cards for mulligans you must announce how many cards you are going to draw, up to the maximum allowed. If you don't announce a number ahead of time, then you must draw the maximum amount. You don't get to look and decide as each card is drawn.
Source: TPCi Rules Team (2015-11-19)
When my opponent fails to draw a Basic Pokemon in their opening hand do I have to draw my card right away, or can I wait to see if there are more Mulligans before drawing my cards?
The Advanced Rules section of the current rulebook indicates the player who did not start over may draw a card for each additional time his or her opponent took a mulligan *after* the player with no Basic Pokemon finally draws a Basic.
Source: TPCi Rules Team (2013-01-03), TPCi Rules Team (2013-11-21)
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)
My opponent MUST put their basic down first before they draw 1 card for my mulligan, right? Say my opponent draws a better choice starter Pokémon when I mulligan, are they allowed to switch it out with another from their hand?
They must place their active Pokémon and their prizes before optionally drawing a card for the mulligan. Once placed, the active cannot be changed during setup; but you are allowed to add a new Pokémon to your bench, if there is room.
Source: PUI Rules Team (2005-06-16), PUI Rules Team (2006-02-09), PUI Rules Team (2006-07-27)
Before starting the game, Player-A has a Basic Pokémon but Player-B does not. On Player-A's draw 1 card for mulligan, say they draw a better choice for starting Pokémon; are they allowed to switch it out with the one they chose to be their 1st active before the mulligan? And if they choose to switch, must it stay on the field and not allowed to be put back into hand?
Player A continues his or her setup and can choose to draw an extra card after setting aside his or her Prize cards. Once placed, the active cannot be changed during setup, but a mulligan card can be placed onto the bench.
Source: PUI Rules Team (2005-05-05), PUI Rules Team (2006-02-09)
In a sanctioned Tournament, does the player have to show his hand in the event they have no Basics at the start of the game? The Floor Rules don't explicitly say that they have to.
Yes, you still reveal your hand before you shuffle it back into your deck. The rules from the rulebook still apply unless specifically stated otherwise.
Source: PUI Rules Team (2003-10-16), PUI Rules Team (2006-01-26)