Procession does not have an "If you do" clause. Imagine if Procession's card text read, "You may play an Action card from your hand twice. Trash it. Gain an Action card costing exactly $1 more than it." Thus you still gain an Action card costing $1 more than Pillage even if Pillage is already in the trash.
Pillage also does not have an "If you do" clause. It reads, "Trash this. Each other player with 5 or more cards in hand reveals his hand and discards a card that you choose. Gain 2 Spoils." Thus you affect your opponent once (assuming he has an initial handsize of 5 cards) and gain 4 Spoils.
Counterfeit/Spoils is mentioned in the DA rulebook. According to the card text on Counterfeit, you play, and then you trash the treasure. The card text on Spoils indicates that you return the card to its pile immediately upon play. Thus Spoils does not get trashed, but returned to its pile instead, but it is also played twice. (If I remember correctly. I remember playing with this combo against Turambar and loppo at GenCon and specifically checked the rulebook to confirm the interaction. It was a Marauders game and our junked decks made it difficult to get to $8.)