If a player earns a penalty for "failing to set up Prize cards at the beginning of the game", would playing Acro Bike or Great Ball count as a search for escalation purposes?
A search is classified as an action that occurs following the direction of card text "Search your deck...". It does not include "drawing cards" for things like Acro Bike, nor "looking at the top/bottom X cards" for things like Great Ball, due to the drastically reduced portion of the deck that is accessed.
Source: TPCi Rules Team (2019-03-28)
When searching my deck, at what point can I no longer change my mind on which cards I am choosing?
When something says to search your deck for cards you should search the deck, make your choice, and shuffle afterward. Once you begin shuffling you may not go back and change your choice unless your opponent allows you to do so.
Source: TPCi Rules Team (2017-07-06)
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)
Could I use a Poké-POWER, Poké-BODY, Attack, or Trainer to search through my deck for a particular card if I already know that card is not in my deck (i.e. using Energy Search if you know there are no basic Energy left in the deck due to previous unsuccessful searches)?
Yes you may, but if done repeatedly a judge may evaluate whether it's being used legitimately or merely as a stalling tactic.
Source: PUI Rules Team (2005-12-08)
Is a player allowed to count the number of cards in his/her deck during a game, provided he/she doesn't change the order of the cards? And if so, is it permissible to count your opponent's deck as well?
Yes, the number of cards in both your and your opponent's deck are public information. Although it is recommended that the player counts his or her cards during their opponent's turn, in a manner that doesn't disrupt or slow down the game.
Source: PUI Rules Team (2004-05-06)