If we are in a Tiebreaker or Sudden Death game, can I use Squawkabilly ex's "Squawk and Seize" Ability on my first turn?
Even though the Tiebreaker or Sudden Death is used to resolve a game where "Squawk and Seize" may have already been used, the Tiebreaker/Sudden Death is considered a separate game on its own so "Squawk and Seize" may be used on each player's first turn.
Source: TPCi Rules Team (2023-12-14)
If it is your first turn going second and you attack with Medicham V's "Yoga Loop" attack, are you allowed to use Squawkabilly ex's "Squawk and Seize" Ability during that additional turn?
No, you cannot. The second turn is a new turn and no longer your first turn.
Source: TPCi Rules Team (2023-12-14)
Due to a localization error in the Brazilian Portuguese version of the Squawkabilly ex card (SV:Paldea Evolved, 169/193), the text of the "Grasnar e Aproveitar" Ability will be updated. The original text of this Pokémon's Ability was, "Uma vez durante o seu turno," ("Once during your turn,"). This Ability was intended to be used only on a player's first turn of the game. The Ability text must be updated to ensure that "Grasnar e Aproveitar" functions as intended, and must align with the original Japanese text. The new text for Squawkabilly ex's Ability will be, "Uma vez durante o seu primeiro turno," ("Once during your first turn,). The change will take effect immediately, and all Brazilian Portuguese versions of Squawkabilly ex (SV:Paldea Evolved, 169/193, 247/193, and 264/193) will use the updated Ability text.
Source: (Jun 21, 2023 TPCi Announcements [https://www.pokemon.com/br/errata-de-squawkabilly-ex-escarlate-e-violeta-evolucoes-em-paldea-169-193-do-pokemon-estampas-ilustradas]; Nov 9, 2023 TPCi Rules Team)
Can I use Squawkabilly ex's "Squawk and Seize" Ability if I have no cards in my hand to discard?
Yes, you always have a hand even if it has zero cards in it.
Source: Paldea Evolved FAQ; TPCi Rules Team (2023-06-08)