Sounds like a Bais Midrash here.
In regards to a woman uncovering her hair at home. If I remember correctly, the Magen Avrohom states that one shouldn’t uncover her hair even at home. He cites either Kimchis or a Zohar (maybe even both). I believe that it is in Orach Chaim 72, however I’ll try to bring an exact when I get my hands on a Shulchan Aruch. There might also be a Darkei Moshe (possibly in Even HEzer) that rules the same.
In the Gemara (the way most Rishonim explain) it isn’t really an issue. The question of a ‘Kalsa’ (net) is only in public. However, the Chasam Sofer does maintain that even in the privacy of her home it is considered ‘Overes Al Das Yehudis’ (here too you’ll excuse me for forgetting the exact – I’ll get it all in a later post IY”H). Reb Moshe argues on the Chasam Sofer in the Igros Moshe (I believe E”E Chelek 1 Siman 58, I’ll give you this too), but still says that one should refrain after a Psak has come out of the holy mouth of the Chasam Sofer.