What are the valid excuses for abstaining from congregational prayer in the mosque?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
Concessions (Rukhsah) are granted to abstain from congregational prayer in the mosque due to general excuses, such as: rain that causes hardship in going out, strong winds at night, heavy mud that cannot be traversed without the risk of soiling oneself, hot winds, and extreme heat or cold. There are also specific individual excuses, such as: illness that makes walking as difficult as walking in the rain, severe drowsiness, evident hunger or thirst, the suppression of bodily wastes (urine, stool, or gas), and fear for one's life, limb, physical faculty, wealth, or honor, among other valid excuses. And Allah the Exalted knows best.
What is the ruling on water present on the floor of a toilet/bathroom?
The default ruling is the purity of this water present on the bathroom floor. If one is certain or strongly suspects its impurity, then one washes whatever part of the body or clothing this impure water has touched. If one doubts its impurity, the default is purity, and we do not rule it impure based on mere doubt. And Allah the Almighty 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).
What is the ruling on performing ablution (wudu') and ritual bathing (ghusl) with Zamzam water?
It is permissible to perform ablution and ritual bathing with Zamzam water. However, scholars disliked using it for cleaning after relieving oneself (istinja'). And Allah the Almighty knows best.