Is it permissible for a menstruating woman to enter the mosque for the purpose of studying or teaching therein?

All praise is due to Allah alone, and may His peace and blessings be upon His Messenger, his family, and his companions.

It is permissible for a woman to put kohl on her eyes and adorn herself for her husband, as long as it does not involve anything prohibited by Allah, such as showing it to non-mahram men.

As for removing hair between the eyebrows, it is permissible because it is not part of the eyebrows that the Prophet (peace be upon him) forbade plucking. The hair between the eyebrows is like the hair on the rest of the face and body, and removing it is not considered namṣ (plucking). Namṣ is specifically the plucking of the eyebrows themselves, which alters Allah's creation, and that is forbidden.

Ibn Taymiyyah (may Allah have mercy on him) said in Majmū‘ al-Fatāwā (21/189): “Namṣ is plucking the hair of the face.” Then he said: “And it is said that namṣ is specific to the eyebrows.” This latter opinion is the more common and well-known understanding among the jurists and linguists.

And Allah knows best.