Would a woman be permitted to write a sefer Torah? I understand that it is not done (at least in Orthodox circles), but would doing so violate any halacha? What about the general catch-all of kevod ha'tzibbur?
The Shulchan Aruch (YD 281:3) writes that a woman who writes a Torah scroll invalidates it:
ספר תורה שכתבו מסור, עבד, אשה, קטן, כותי, ישראל מומר פסולין.
The Aruch Hashulchan (YD 281:1) writes the reason from the gemara:
וכך שנינו בברייתא:
ספר תורה תפילין ומזוזות, שכתבן עבד אשה וקטן, כותי, ומלשין, ומצרי, ועבריין – פסולים. דכך גזרה התורה, דכל שאינו בקשירת תפילין, או שלא נצטוו, או שפרקו מעליהם עול מלכות שמים – אינם בשום כתיבה.
I found this useful article that has a pretty comprehensive analysis on the issue. I will edit in some additional info, IY"H, when I have more time. For now, I am citing part of the conclusion / summary from the article.
In summation, there is certainly no basis to allow a sefer Torah written by a woman as valid either le-khathilah, or, in reliance on Rambam, bi-she'at ha-dehaq. The most that can be said is that if one does read from such a Torah, it is no worse than reading from sifrei Torah with other disqualifying flaws, and such a person fulfills his obligation be-di-'avad.
To understand the context of the above citation, much of the rest of the article focuses on distinguishing between a woman writing a Torah for the purpose of writing a Torah (one mitzvah in itself), which would be permitted (according to most opinions) vs. her writing one for the purpose of congregational reading (most opinions object to this.) The reason for the objection, here, is based on whether women have an obligation to hear congregational Torah reading. Add to that a general rule that someone who cannot fulfill others in the mitzvah cannot be involved in the mitzvah. Based on combining these 2 ideas, many claim that a woman cannot write a Torah for congregational reading.
However, even that opinion is somewhat ambiguous, and it's discussed more in the article. As stated, I'll try to edit in some relevant parts, later.
If a man writes the 5 books of the Torah on separate scrolls ("Chumashim") and then sews them together, he has created an entity which is greater than the sum of its parts. The new full Torah has a higher level of sanctity than just a Chumash.
However if a woman does the same thing, the new object does not have the higher holiness of a Sefer Torah but is just a Chumash that happens to have all 5 books in it. (The Drisha (YD 281) argued on this, but the Shulchan Arukh (ibid. :3) and most later authorities reject him.) What she did is completely permitted, but it's not effective in the way she may have intended. This scroll wouldn't fulfill the biblical commandments of writing a Torah scroll (Chinukh #613), reading from a Torah scroll on Sukkot following Shemitta (#612), or a king writing a Torah scroll (#503), nor would it get the same level of respect (#257) as a kosher Torah scroll such as when stacking scrolls (YD 282:19) or according to some standing when it is in movement (ibid. :2).
Regarding using it for the rabbinic enactment of regular public reading, there is extensive Halakhic literature in the Beit Yosef OC 143 and YD 279 (in the context of mistakes found during Torah reading) about using a Chumash scroll for Torah reading and more generally using Torah scrolls with non-apparent problems, and, as any synagogue rabbi will tell you, the range of positions is vast. Generally speaking, there might be some room for leniency, particularly for Ashkenazim, if this were the only scroll available (per the end of the Rama OC 134:4 quoting the Ran), and very likely the reading wouldn't need to be repeated if it had already been accidentally read from (per the custom in the Rambam's famous responsum, accepted after the fact by the Shulchan Arukh OC 134:4). But there's essentially no room to allow using such a scroll in a Lekhatchila situation. We're talking highly controversial minority opinions here for very Bedieved situations only.
In the end of the day, while such a scroll could certainly be used regularly for personal study, with the ubiquity of printed works it really just seems like a big waste of time. Plus you'd have to be very careful (cf. YD 281:1 with Taz, etc.) to ensure it doesn't get mixed up with identical looking Sifrei Torah written by men. If a woman wants to write STaM, she'd be much better off spending her time writing Nevi'im or the like for actual regular use in synagogues.