1) It is prohibited to daven in a Shul that does not have a [Kosher] Mechitza (separation) between the men and the women.
Even if the women are dressed modestly, it is still prohibited to daven without a Mechitza. The Poskim say that it is better to daven without a Minyan than to daven in a Shul that lacks a Mechitza. (Many even prohibit davening in a side room of such a shul)
Rav Moshe Feinstein (Igros Moshe Orach Chaim Vol. 1 Siman 39) and others maintain that a Mechitza in a Shul is a biblical obligation, regardless of how modest (or G-d forbid immodest) the women are dressed, as not having the separation may lead to a lightheadedness between the sexes, and may lead to touching and/or excessive talking.
Rav Moshe adds that these Halachos are not only pertinent during davening, but also at any gathering in the Shul (funeral, Simchas Torah, Simchas Bais HaShoeva, Sheva Brachos etc.)where men and women are present, a Mechitza must separate them.
from halachafortoday