Is it permissible to trim the eyebrows if they become excessively long?
Trimming eyebrows is permissible if they become excessively long, yet; it is reprehensible. And Allah Knows Best.
Is it permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?
It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).
Is it permissible for a wife to refuse to go to bed with her husband (for sexual intercourse)?
It isn`t permissible for her to do so unless for a sound reason.
What is the ruling on taking a medication tablet sublingually during the daytime in Ramadan?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Taking a medication tablet sublingually (under the tongue) during the daytime in Ramadan does not invalidate the fast, since it does not reach the internal cavity (al-jawf) through an open passage.
However, if the tablet dissolves and any part of it is swallowed, then the fast is broken.
And Allah, the Exalted, knows best.