This is how I'm interpreting the new cards with errata, hoping it's correct.
Haunted Woods, Swamp Hag, Haggler: If you are Possessed and buy a card, neither you nor the Possessor gets the when-gain ability.
Messenger, Defiled Shrine (gaining Curse), Tax: If you are Possessed and would gain the card in your Buy phase, neither you nor the Possessor gets the when-gain ability.
Overpay cards: Both Ingix and
Donald have said that you do the overpaying when you pay for the card, so it seems to not be timed as when-buy (which happens after you bought the card), but rather before that. So if you play with old Charm and buy a Herald, you can't gain a Silk Merchant or Nomads before overpaying in order to have more $ to overpay with.
Overpay is: you get the when-gain ability based on the amount you overpaid. If you are Possessed and buy an overpay card, neither you nor the Possessor gets the when-gain ability.
(Using Trader v.1 would of course work the same as being Possessed.)