Generally, Orthodox families do not make a huge fuss with Bnot Mitzvah ("B'not being the plural of "Bat") - at least not on the same level as a Bar Mitzvah. That means, that there is usually no festivity done in a synagogue. (Within the past decade or so, that has been changing very slightly, as some Modern Orthodox have started doing at least some small celebration in the synagogue. However, among the "black hat" crowd that you describe, I know no one that has done anything in the synagogue.)
The girl does not read from the Torah at all. - certainly not in synagogue during services. She may give some small speech thanking her parents, siblings, relatives friends and others for attending and making significant contributions to her life.
A "black hat" crowd of people always dresses modestly. Most of the men will probably be wearing suits and black hats - esp. rabbis who will be attending. (BTW, expect that the rabbis esp. if they are affiliated with the girl's yeshiva will probably be making speeches and saying words of Torah.) The women will also be dressed modestly and many will be wearing wigs, hats, or covering their hair, otherwise.
If you're considering a nice gift for the girl, I think a small Siddur, Tehillim, a kerchief (as she may eventually use it when lighting Shabbat candles or to cover her head, otherwise, once married) or small candle sticks, may be appropriate. Judaica-themed jewelry, of course, always works.
I don't advise bringing any food items unless you ascertain which kosher certifications the household uses.
I couldn't determine your gender from your user name, so, at the moment, I can't advise you how to dress other than to say "modestly". If you're male, wear a suit, nice shirt and tie. Female - dress long sleeves and at least a hat. I.e. - don't dress in any pants, shorts or bathing suit, etc,
I hope this helps.