I think Abigail is the Wizard's daughter. And I think Caroline didn't cheat on Pierre either.
The evidence for Abigail being M. Rasmodius's (which I think is a title and stands for Mage or Magister but that's a separate conversation) daughter is clear: she claims to have not dyed her hair in some time and it remaining purple, the same hue as the Wizard's;
Pierre asks the farmer if she "looks anything like [him]" and says he suspects he's not the father (though this could simply be a result of the jealousy issues Caroline ascribes to him);
Caroline says she spent time near the Wizard's tower when first moving to Pelican town and conceiving Abigail after 2-4 months (allowing for premature or late birth) in town;
the Wizard outright admits that he suspects one of the locals to be his daughter and that his wife left him after an unspecified "mistake" (a common excuse for infidelity, despite a drawn out and actively hidden relationship being quite a bit more work than most mistakes).
Of the marriageable villagers, only Abigail and Penny have the possibility to be the Wizard's daughter, with the unknown father of Penny, while Emily, Haley, and Leah being from out of town makes them unlikely and Maru resembling her father. Jas is another possibility, being Marnie's niece (though having lived with her since a very young age, as evidenced by Secret Note #11), having purple hair, and her home being near the Wizard's tower. However, Jas presents as an entirely normal young girl (despite a somewhat troubled home life) and closely resembles her cousin Shane's dark-purple hair, indicating a family trait. The Wizard only mentions a daughter, not a son. If he had had a child with Shane, then Shane would more easily claim her as his daughter, not goddaughter. Penny has no resemblance in looks or demeanor to the Wizard, and though that is possible in families it would also not give him reason to suspect her.
There are a few things that stand out to me. First, Caroline admits to having spent time near the Wizard's tower in the time Abigail was conceived- something she would be unlikely to admit if she had been having an affair, placing herself at the "scene of the crime" as it were. Second, she says she wishes Abigail would "stop" dyeing her hair, and that it resembled her grandmother's hair, "light chestnut-colored hair", like Pierre's.
Abigail confirms that the purple was not her original color, but that "it never fades from this color". But what makes me think the Wizard didn't cheat on his wife is the line, "It's rare, but it does happen." He could be referring to a birth control method failing, but frankly I'm dubious that a small town could have a woman become pregnant with no available father and have no one comment on it (such as Marnie, with no mention of past partners). The gravestone for Mona makes no mention of motherhood, which is almost inevitable on women's gravestones, which makes her unlikely in my eyes, and if she were his "other woman" it would be fairly obvious to him.
The fourth uninteractable gravestone gives us no information and so must be disregarded. I think that Caroline's time near the Wizard's tower during her conception time frame exposed Abigail to the Wizard's magic and contaminated (for lack of a better word) her. His magic changed her, making her his child just as much as Pierre's and Caroline's. Caroline would have no reason to suspect this, and so no reason not to admit to the farmer she was near the Wizard's tower. Pierre would notice that his child resembled another man, despite her similarities to him while younger, and draw conclusions. The Wizard would be unsure of it (while having had sex with the mother would make it very likely) and have reason to comment on its rarity. The Wizard's wife left him after a "mistake"- perhaps a mistake like not containing his magic enough.
And what curse does she cast on the farmer? Putting a strange, changed chicken in their nests, and changing their slimes unnaturally.
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