Player A attacks and flips a heads for "Agility". Then Player B uses Single Strike Urshifu VMAX's "G-Max One Blow" attack; would this ignore Agility?
In this case, Agility would be considered an "effect on the Defending Pokémon" and therefore G-Max One Blow would be able to overcome Agility.
Source: PUI Rules Team (2005-02-17); TPCi Rules Team (2021-05-13)
If I flipped heads on Seadra's Agility attack, would that prevent Cradily's Spiral Drain from removing damage counters?
Agility only prevents damage and effects done to Seadra, not other effects that may extend to other Pokémon.
Source: PUI Rules Team (2004-03-25)
If a Raichu (or whatever) does Agility and flips heads, does an attack that would do damage to benched pokemon, or some other effect that does NOT do damage or something to Raichu work?
Yes it would, while all attacks are considered against the defending Pokemon (which is why something that prevents attacks would stop it in this case), Agility only prevents the effects of that attack if they affect Raichu only.
Source: WotC Chat (2001-07-19)
If my Pokémon uses Agility and get heads then on my opponent's next turn he benches his Pokémon, does that [Ed. Note: Agility's effect] end? If that Pokémon was Knocked Out, would Agility still be on the next Pokémon that he sends up?
Since the Agility Attack references Rapidash, only Benching or Evolving him ends the effect. Also since it only refers to Rapidash it would still be in effect if the other player benched.
Source: WotC Chat (2000-06-30)
When using Raichu's Agility attack it states that if heads, Raichu will not receive damage until after the opponent's turn. If Raichu is poisoned and then gets heads, will he take damage from poison at the end of his turn?
Yes, Agility is referring to effects of attacks on Raichu during your opponent's next turn.
Source: WotC Chat (2000-06-01)
Does Fearow's Agility attack block Kangaskhan's Fetch?
Actually it does not; Fearow's Agility says stops damage done to Fearow, and the Fetch just draws a card. This is the new ruling from R&D.
Source: WotC Chat (2000-02-03)