M’ikar ha-din may someone daven in a place where there is no mechitzah (b’ofen that there is no shailo of seeing any ervah of any of them women.) What’s the makor in halacha for having a mechitzah?
The two basic sources are the Gemara in Sukkah (51b) concerning the Beis Ha-Mikdash, and the Gemara in Kiddushin (81a) where an anecdote is mentioned concerning the separation of men from women at public gatherings.
Rav Moshe Feinstein (1:39) understands that there is full obligation to make this separation, including a partition (and not merely a separation), and applies it to every gathering where men and women are present. In his opinion (based on Rashi and the Rambam) the purpose of the mechitzah is to prevent mingling and kalus rosh. Others argue that the purpose is to prevent improper thoughts, the practical difference being of course the quality of the partition.
There is no formal obligation on davening in a place without a mechitzah, so that if one has to daven in a makeshift room, and there is no mechitzah, there is no prohibition of doing so.
However, one must not daven in a place where there is no mechitzah on a permanent level, for this would imply granting legitimacy to this forbidden practice which runs contrary to a well-known halachah.