Family member of ex-Ultra-Orthodox here, so might be able to answer a few questions.
Although @Lynda07 is right, the sect Etsy belonged to (Satmar) is not Chassidic, they are Charedi which is very different from the more outgoing Lubavitcher sect.
All of these 'Courts' as well as the many other sects come from one main founder, the Baal Shem Tov. These are almost like dynasties with the same power struggles you'd find in corporations. Usually when the Rav or Rebbe (the senior guy at the top) dies it's a son who takes the seat, but sometimes there isn't a son so a trusted second in command takes the seat. Here's where the decimation happens because if the community don't like / agree with the new Rav they form another Court around whom they think should've inherited the role.
The Lubavitch are the most outgoing of all the 'Ultra-Orthodox' this term is problematic to most as they don't see themselves as such, this is 'the right way' and the rest of us Jews are mostly apostates 
I mentioned the Lubavitch due to their outreach work trying to bring us Reform / Liberal and secular Jews back to the more traditional forms of practicing Judaism. You see a lot of them in NYC approaching any men who look remotely Jewish and asking them when they last laid tefilin (the little boxes wound around the left arm and the forehead). When a Jew returns to this kind of traditional Judaism and religious observance they are called Baal T'shuvah which literally means 'returned'.
Each court has its own style of dress, which if you are in the know is interesting to spot. The Lubavitch boys and men wear black fedoras usually Italian Borsalinos, but there are other sects in Israel who also wear fedoras but the brim is of different width, or they wear the band of the hat a different way.
The large mink tail hats are called Streimels and are only worn on Shabbes (Shabbat) weddings and festivals. I have seen a huge plastic streimel filled with popcorn worn for the Jewish festival of Purim, the one time Jewish men (it's always the men) can get drunk and cross dress.
Then there's the long white socks worn on Shabbes and these tend to be Satmar men who wear them but there is another court of Belz who wear long black socks and white kippot (little skull caps) that have a long tip sticking up from the crown.
The payess (peyot - long side curls) do indeed come from the Torah commandment of not cutting corners on hair https://www.ou.org/torah/mitzvot/taryag/mitzvah251/ but not all sects follow it the same way, some wear them long, some tuck them up and some keep them short. There are approximately 613 mitzvot or commandments you have to keep if you are an observant Jew and these cover everything! Especially family purity as demonstrated to Etsy before her wedding day in her Kallah (Bridal) classes. A rabbi has to inspect these cloths if there is any confusion over spotting and there is a pigeon hole for this outside of his office.
The women have their own set of dress rules. When I'm in Macy's or Kate Spade in the Rockefeller Centre I usually see them with their families. The married ones will be wearing their sheitels (wigs) usually in similar styles, dark clothing, bulletproof stockings, flat or flatform shoes (the sound of a woman's high heel is considered too alluring) with little silk pillbox hats on their shiny, natural hair wigs. They will be talking in Yiddish but will switch to English when asking for assistance.
It's a tough existence to live if you are different by wanting more out of life. Particularly if you were Satmar, they strive to be the most vigorous adherents of the commandments, hence the shaving off of women's hair. Nowhere in the Torah does it specify this has to happen. Even in Talmud (the many books of Rabbinical commentary of the Torah). To me, as someone very close to it, these sects are almost cultish with their deference to a particular leader or place, the non exposure to wider information ie education, news, music, radio, books etc.
Sorry, I've really rambled on! 