Ames, you can’t make a bracha at any time for no reason unless you leave out Hashem’s name. Women are permitted to say the bracha with Hashem’s name if they are actually performing the mitzvah at the time because a) it’s a statement that Hashem commanded Bnai Yisrael as a whole with the mitzvah, and b) the bracha is applicable to the mitzvah currently being performed. Is that clearer?
Squeak, I do know women who stay up to learn in their living rooms. (This makes childcare easier because they can just get up to go to the baby’s room when they hear it crying, calm it down, then go back to learning.) However, learning is always better in chavruta or group settings. Women who gather together to learn are gathered so as to enhance the learning experience all around, and even if it’s in a public setting, it’s not like we’re talking about a co-ed learning environment. I don’t see why a group of women getting together to learn Hashem’s Torah should raise a red flag. Are women suspected of “trying to prove something” every time they leave their houses now?