At the Sabbath meal the assembled group dances to a "niggun" (wordless melody) that is traditional among Lubavitch Chassidim. It is usually sung as a preparation to one of the Rebbe's discourses being repeated from memory, though; not as a slow circle-dance.
The Ariel character has a neatly trimmed and partially shaved beard, while explaining payes (side curls). Ultra-Orthodox Jews do not shave any part of their beard or neck.
The shot of the newsstand shows the Israeli newspaper "Ma'ariv". The movie takes place in the Williamsburg section of Brooklyn, home mainly to Chassidim of the Satmar dynasty who have been extremely anti-Zionist since the mid 20th century and probably not customers of "Zionist entity" publications. Also, the English-Jewish paper "The Jewish Press" is on display. Since Yiddish is the first language of most Williamsburg chassidim the main papers on display should be in the Yiddish language; Der Yid and/or Der Blatt are the preferred reads.