Curiosity: Good questions. Here’s the answer about women. From a Breslover website:
“Some newcomers to Breslov assume that the Rosh Hashana gathering in the city of Uman, near Rebbe Nachman’s gravesite, was always a ‘for men only’ event. However, prior to the Stalinist purges, women also attended prayer services in the Breslover Kloiz on Rosh Hashana, as well as on Shabbos and the Yomim Tovim. In fact, it was the personal custom of Rav Avraham Sternhartz, the Baal Tokei’ah and Baal Musaf, upon leaving the synagogue to offer holiday greetings to the women waiting outside for their husbands and sons.
The main reason women today are discouraged from traveling to the Rosh Hashana gathering in Uman is because under present circumstances, it would be impossible to accommodate large numbers of women without serious breaches of tznius (modesty). However, groups of women travel to Uman throughout the year, where they, too, recite the Tikkun HaKlalli, the ten psalms prescribed by Rebbe Nachman to heal the soul.”