If Shiftry uses "Feint Attack" against a Pokémon that successfully used "Agility" the previous turn, would Agility prevent the Feint Attack or not?
No, the Feint Attack ignores any effects on the Defending Pokémon, including Agility, Wonder Guard, etc.
Source: PUI Rules Team (2004-01-08)
I've noticed that some cards say "Does 10 damage to the Defending Pokémon", whereas others say "Put 1 damage counter on the defending Pokémon". Is there any reason for the different wording? I've spoken to someone who says that you do not apply weakness or resistance for attacks where it specifies Damage Counters; is this the case?
There is a difference. As you mention, weakness and resistance are not applied when placing counters. Also, things like Defender and Metal Energy will not block Placing Damage Counters. It will not trigger things like Base Set Machamp's Strike Back. In the steps of resolving an Attack, "placing Damage Counters" counts as an Effect of the attack, it is not part of "doing damage".
Source: PUI Rules Team (2003-09-18)
ANY Pokemon attack or Power that can only be used once per turn, is reset if that Pokemon evolves or devolves or leaves play and that power or attack could be used again if that Pokemon came into play again that same turn. The "can't use this attack next turn" sets up a status effect that can be ended through the normal means: benching, leaving play, evolving or devolving. With Pokemon Powers though, you can't get around the once per turn by benching. Benching a Pokemon does NOT get around these effects as they are still the same Pokemon and still in play. [Ed.Note: This does not apply to Tentacool Lv.10 (Fossil) which specifically states in the text of the power that it cannot be used on the same turn it comes into play.]
Source: WotC Chat (2001-09-27), WotC Chat (2002-02-14), WotC Chat (2002-05-23)
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)
It has been ruled that W/R does not apply to the bench unless specifically mandated by the card. Period. That is a meta-game rule. It was never intended that the W/R would apply to the bench unless specifically stated. Yes we do know that some Pokemon say not to apply W/R to the Bench. [But] if it doesn't say then you wouldn't apply Weakness and Resistance (the default for benched Pokemon is to NOT apply Weakness and Resistance). This has been verified.
Source: WotC Chat (2001-05-03)
If Wooper uses Amnesia on Scyther's Slash, then Scyther retreats for another Pokémon, then that Pokémon [is Switched] for Scyther again, can Scyther use Slash?
Amnesia references the defending Pokemon, when that Pokemon is benched the effect ends.
Source: WotC Chat (2001-04-12)
If your Pokémon has been Smokescreened on the previous turn, and you choose an attack that requires you to do something (such as discarding Energy) in order to use the Attack, do you pay the attack costs before you flip for the Smokescreen Effect?
Yes before, you still attempt the attack; the Smokescreen might just stop it from having any effect.
Source: WotC Chat (2000-04-13), WotC Chat (2001-04-05)
Say you are using a Golduck (from the Fossil set) and you use his Psybeam. Would this be a Psychic or Water attack?
A Water attack as Psyduck is a Water Pokémon. [Ed. Note: This answer can be generalized further: When a Pokémon attacks, that attack is considered to be an attack of that Pokémon's type; it's not dependent on the energy requirement.]
Source: WotC Chat (2000-08-31)
When a card's attack "does damage to itself", is this damage considered to be an ATTACK against the Defending Pokémon? Let's say you had an Electabuzz versus a Team Rocket Porygon and Team Rocket Porygon switched Electabuzz's Weakness to Lightning. You Thunderpunched with Electabuzz and flipped tails. Would Electabuzz receive 10 or 20 damage? Furthermore, would Defender prevent this damage? (Defender prevents damage from attacks).
1) 20, it is considered an attack. 2) Well, assuming it was an attack that did damage to itself, then Defender would help with that damage.
Source: WotC Chat (2000-08-03)