>Doubles money received after battle if the holder takes part in the battle. Once the Pokémon has participated in battle while holding it, it cannot be negated; it takes effect even if the holding Pokémon faints or the Amulet Coin is stolen, knocked off, flung, or negated.
The Amulet Coin activates as long as the Pokemon holding it participated in the battle, it doesn't even matter if it fainted or if it lost its Amulet Coin in the battle.
As well as the Luck Incense, however, it does not stack with Amulet Coin.
As for your second question, neither the Amulet Coin nor the Luck Incense stack, so the result will be the same as if you only had one Amulet Coin/Luck Incense.
>Does not stack with Luck Incense or other Amulet Coins.
Happy Hour does stack with Amulet Coin/Luck Incense, so the money would be 4x the amount(to answer your example, you would receive 4000 Pokedollars after the battle).
Sources: links above and Happy hour