Bob,
1. She was Bathya (pronounced as Batya, the second letter in Hebrew is tav, which is "T" in Hebrew, but "S" in Yiddish (gut shabeS)
2. She was Batya BAT-TSIYON, I think it is her surname and doesn't mean she was  Tsiyon's daughter.
3. she was "daughter of Yaakov-Moshe HAKOHEN"
4. do you know the surname of the husband Yehuda Lejb s/o Tsvi? Wasn't he BEN-TSIYON? BAT-TZLYON?
5. the status of cohen nobody "earns", it comes from the father and cannot be "lost". (should ask some Rabbi, if I am right in this point )

Josef ASH, Israel