Is a nidah allowed to hold a sefer Torah? Can she & other women, particularly women who learned Torah the entire year, dance in the Ezras Nashim with a sefer Torah?
It is permitted for a woman to hold a Sefer Torah, and to dance with it, even if she is a Niddah.
Some are stringent not to gaze at an open Sefer Torah during the Niddah period, and this will possibly apply to holding the Sefer Torah too (see Orach Chaim 88 and Mishnah Berurah 7).
However, this is a stringency, and where the women will gain spiritual uplifting and fulfillment from dancing with the Torah, one can be lenient for this matter (see Shulchan Aruch, Yoreh De’ah 282:9; Or Zarua 1:360).
Some authorities are specifically lenient where a woman donated the Sefer Torah, and if the women learned the Torah their connection with it is surely no less.