I found it helpful to look into the multiple forms and how this fits into a pattern that is easier to remember. I hope you find it useful.
celui (masc sing); celle (fem sing) = the one
ceux (masc pl); celles (fem pl) = the ones
celui-ci (masc sing); celle-ci (fem sing) = this one
ceux-ci (masc pl); celles-ci (fem pl) = these (here)
celui-là (masc sing); celle-là (fem sing) = that one (there)
- ceux-là (masc pl); celles-là (fem pl) = those (over there)
[Edit] I feel compelled to add that the "here" and "there" shown in these references are NOT spoken or written in proper English. I included them only for the purpose to help us consider how to refer to things that may be either nearer to us or farther away.
Yes, I think it is what we would be more likely to say - although, strictly, we should not follow a preposition (for) with nominative case (she). For her is grammatically correct, but sounds awkward. All in all, it's probably better to recast the sentence as For the woman who likes to write or some variant thereof.
Actually you can. If it is important to use the feminine "celle" in French, e.g., a marketing campaign targeting women, then you may carry it into English by using a feminine pronoun. Since "her" cannot be used as the subject of a sentence, we would say "for she who likes to write". Since the French must use either "celui" or "celle", then you can allow flexibility to say "for the one..." If you insist on it being gender-specific, then you must be aware that English speakers will need to improvise in order to convey that. Hence MaPfe's suggestion of "for the woman...." Not everything is going to translate precisely in both directions. Better: "For the one who likes to write".
I put "for her who likes to write," because "her" is the object of "for." It is qualified by the relative clause "who likes to write," whose subject is "who," but that clause has its own syntax. The "her" version sounds hella unnatural, but is certainly correct, formally.
No, that's wrong. The relative clause is "who likes to write." The word "who" is its subject, which is why it's "who" and not "whom." The word "her" is the object of "for," which is why it's "her" and not "she." The relative clause modifies the pronoun "her," but doesn't alter its case.
Does this sentence merely mention that the person who likes to write is female, or does it emphasize it? Unless it's emphasis, "the one who likes to write" is correct. "The woman" or "the girl" may be more precise, but that doesn't make "the one" wrong.
Also, "she who likes to write" may be correct, but it's also archaic usage and therefore not preferable. Unless you're trying to sound like a proverb.
The "wrong" use of "one" according to the red you-are-incorrect message where I clicked on the discussion to see why and found "one" in the translation at the top of the page was not on this page - it was in the lesson on infinitives, I believe. But DL is a valuable resource. I should not complain too loudly. DL's "for she" blunder just reminded of the earlier irritation.