Trainers » Wally
Wally says "you can use this card on your first turn or on a Pokemon that was put into play this turn". Does that mean I can use Wally on the very first turn of the game when I am not allowed to play Supporter cards?
No, Wally does not override the game rule of the player going first not being able to play Supporter cards on their first turn. You can only play Wally on your first turn if you are going second.
Source: TPCi Rules Team (2021-02-04)
Trainers » Evosoda | Trainers » Wally
Can I use Wally or Evosoda on a Snorlax to search my deck, even though there is {currently} no evolution of Snorlax?
No, there has to at least be the possibility of a valid evolution in order to use this card. Sorry.
Source: TPCi Rules Team (2018-07-26)
Trainers » Evosoda | Trainers » Wally
Can I use Wally or Evosoda to search my deck for a card that is not in the current tournament format? For example, could I use it on Raichu to search for a Raichu BREAK after it rotates out?
Yes, you can. Even though a card may not be in the tournament format it still exists and can be searched for even though it is known to fail.
Source: TPCi Rules Team (2018-07-26)
Trainers » Evosoda | Trainers » Wally
If I use Evosoda to evolve my Basic Pokemon into a Stage 1, can I then use Wally to further evolve it into a Stage 2 on that same turn.
Yes, but be careful of the order in which you play the cards. Wally says you can use it on a Pokemon that was put into play this turn, but Evosoda says you cannot use it on a Pokemon that was put into play this turn. So you can play Evosoda first then Wally, but you cannot play Wally then Evosoda (on the same Pokemon, of course).
Source: TPCi Rules Team (2017-03-16)