Whether a card's effect is optional or not is determined from the card text. If there is no explicit indication that you have a choice, then you don't have one and the effect is mandatory.
If Pidgeot attacks with "Headwind" against Yanmega with the "Insight" Poke-BODY, will "Headwind" increase Yanmega's attack costs or will "Insight" reset them to zero?
If an Attack Cost is set to zero by an effect, it cannot be increased. Note this is different than an Attack Cost that was reduced to zero by subtraction. Once a Pokemon's Attack Cost is set to zero by an effect, it stays at zero until that particular effect wears off.
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.
In Germany we have two different Trainer Cards with the same translation for the name. Both Energy Retrieval and Energy Returner are called "Energie - Rückgewinnung". How would this be handled in a Decklist? Can I have 4 of both?
In Japanese and English those are two different cards with completely different actions. You may have up to 4 of each in your deck, but on the decklist you should list them on separate lines and include the set and card number on each line for clarity.
Can I have 4 copies of each Alph Lithograph card in my deck?
No, you may not. Each variant of Alph Lithograph does something different, but they all have the same card name. Just like you can have no more than 4 Pikachu in any combination, you can only have a maximum of 4 Alph Lithograph cards in your deck. When entering onto a decklist, make sure to list them on separate lines and include the set and card number on each line for clarity.
When using Boldore's "Smack Down" attack that does 60 more damage if the Defending Pokemon has Resistance to Fighting, does that mean it gets to ignore the Resistance altogether?
No, it does not. You do the Base 20 damage first, then add the +60 damage, and then subtract for the Fighting Resistance amount.
Source:
Emerging Powers FAQ (2011-09-01), PUI Rules Team (2011-09-01)