Quote 1
"And take the Complete Fortune-Teller to the outhouse" […] The Complete Fortune-Teller was an old thick volume, which lay on a table at her elbow, so worn by pocketing that the margins had reached the edge of the type. (3.34-5)
Tess's mother is superstitious about keeping the Complete Fortune-Teller indoors after dark, so they tuck it into the outhouse. Her mother's superstition contrasts strongly with Tess's pragmatic realism, and we discuss that in the "Memory and the Past" theme analysis. But for our discussion of Fate and Free Will, it's interesting that Tess's mother puts so much faith in the ability of this particular book to prophesy Tess's future. Whenever you're reading a book that discusses a book that gets read and re-read until its pages are "so worn" that "the margins had reached the edge of the type," it's a good idea to stop and pay attention.
This is clearly a book that Mrs. Durbeyfield reads frequently. But the trouble is that she's not a good reader. As we learn in the next chapter, the book tells her that Tess will marry a gentleman – that's true. But the circumstances under which she marries the gentleman (and which gentleman she marries) are still fuzzy. Mrs. Durbeyfield doesn't read critically – she interprets what the book tells her in the most superficial possible way, and sees her own desires reflected in the text. Hardy is showing his readers what not to do.
Quote 2
"'Tis nater, after all, and what pleases God." (12.83)
This is Joan Durbeyfield's fatalistic response to the news of Tess's rape. Her response is like the response of the people the narrator quotes in the passage quoted above: "It was to be." Her remark that it's "nater" (i.e., "nature") puts the blame of it on someone other than Alec or even Tess. It's only "natural" that Alec should have taken advantage of Tess. So again, here's another character who's suggesting that fate is stronger than free will, but it's not a character who is particularly trustworthy or reliable. We can't take Mrs. Durbeyfield's words at face value.
Quote 3
"[…] she ought to make her way with 'en, if she plays her trump card aright. And if he don't marry her afore he will after." (7.37)
Mrs. Durbeyfield can tell that Alec is totally lusting after Tess, but she sends her off to work for the D'Urbervilles anyway, assuming that if Alec doesn't marry her "before" (sleeping with her), he will "after."