Islam does not stipulate that a woman should have a mahram with her except in the case of travel. If she wants to go to the mosque or the marketplace or to visit a neighbour or relative, and the place is nearby and the one who goes there is not regarded as being a traveller, then there is nothing wrong with her going there on her own without a mahram. But it is stipulated that the place should be safe, so the route should be safe with no danger to her as she comes and goes.
If the route is safe and the girl can reach the mosque, there is nothing wrong with her meeting with her sisters to do some communal actions such as seeking knowledge, or individual actions such as reading Qur’aan and praying. As for staying overnight in the mosque with her friends and sisters, it is permissible in principle if the women’s prayer space is secure and safe from men entering it or from the foolish trying to overstep the mark with them. That is a matter to be weighed up by the people in charge of the mosque, namely the administration, the imam and the committee that looks after it, as well as parents. Every environment has its own rulings. The most important thing is that the girls should be safe from men entering upon them and the foolish trying to overstep the mark with them. It is preferable for there to be someone who can take charge and take care of them, such as a woman who is a seeker of knowledge (taalibat ‘ilm), so that no fitnah will result from their gathering and so as to make sure they behave themselves in accordance with Islamic guidelines and do not waste their time.
Shaykh Muhammad ibn Saalih al-‘Uthaymeen (may Allah have mercy on him) said: Women may observe i‘tikaaf so long as no fitnah results from their doing so. If it will result in fitnah, then they should not be allowed to do that, because if something that is mustahabb will result in something that is forbidden, it must be prevented, just as if something that is permitted will result in something that is forbidden, it must be prevented…
… But it may be said: How can (a woman) observe i‘tikaaf in a mosque in which prayers in congregation are not held? Is that not a source of fitnah?
The response is that it may or may not be so. This mosque may be safe and secure, and no one enters it, so there is no fear of fitnah for the women if they observe i‘tikaaf there. Or it may be the opposite. The point is that if fitnah will occur, the women should not be allowed to observe i‘tikaaf, no matter which mosque it is.
End quote from ash-Sharh al-Mumti‘ Zaad al-Mustaqni‘, 6/510, 511
It is not permissible for women to raise their voices to the extent that they may be heard by men. If women are forbidden to say tasbeeh (“Subhaan Allah”) to alert the imam if he makes a mistake in the prayer, and they are forbidden to give the adhaan (call to prayer), lead the prayer and deliver the khutbah (sermon), all of which involve dhikr or remembrance of Allah, then it is more appropriate that they be forbidden to raise their voices in other kinds of speech.
Ibn Hajar (may Allah have mercy on him) Women are forbidden to say tasbeeh (to alert the imam to a mistake in the prayer) because they are enjoined to lower their voices in prayer in general, because of the fear of temptation (fitnah).
This is as far as the shar‘i ruling is concerned. However we do not advise staying over in the mosque for the purpose mentioned; we think that it is sufficient for the girls to spend the day there, whether that is studying together or worshipping together, then they should go back to their homes at night.
And Allah knows best.