The date doesn't match because this book was published in 2019, but the story sounds like Curse of the Fae Queen by Delia Castel.
When eighteen-year-old Neara saves a villager from the clutches of a deadly faerie, the Fae Queen sends warriors to abduct her dying father in revenge. To gain his freedom, Neara must venture into the Shadowlands and obtain three enchanted objects under the supervision of the bestial Prince Drayce.
As Neara and Prince Drayce grow closer, she discovers the Queen’s scheme to release an ancient evil and enslave the mortal world. To thwart these plans, she must break the curses of five Fae Princes, but the cost of doing so is her Father’s life.
Torn between saving the human realm and saving her father, Neara must navigate this treacherous world and choose between love, liberty and power.
The village is Bresail and it is a coastal village and there are mists. Specifically the fae cast a mist in order to kidnap Neara's father and force her to come with them:
The next morning, swirling mist, thick as the clouds hovering over the distant mountains, invaded the village. It curled around the rooftops, whirled around the streets. It even obscured the cobblestones, casting everything in white.
The bargain is made between Neara and Prince Drayce:
“I’ll bargain with you.” The words spilled from my lips like honeyed poison. “Leave Father alive in exchange for my maidenhead.”
Drayce tricks Neara because he promises that he will not take her father, but he has two zombie fae take her father instead:
He is coming with us.” He said this with infinite patience, as though we had never come to any kind of agreement to keep Father safe.
“But we bargained—”
“Yes, we bargained. You did not make any such agreements with my deceased friends.”
...
Cold fury swirled through my insides. The wretched thing had planned to take us both all along. “You tricked me!”
“Did anyone ever tell you?” Laughter turned his voice into a low rasp, and leather bindings wrapped around my wrists. “Never bargain with the fae.
The Queen sends Neara on a quest to find:
However, if you wish to save him from an eternity of punishment, you will fetch me three items: the Blood of Dana, the Sword of Tethra,” she tilted her head to the side and gave Father a pointed look, “and the Book of Brigid. Give me those items, and I will give you his freedom.”
