Is it permissible to perform Tayammum for a month due to a medical condition that requires avoiding water?

Tayammum is permissible so long as the above excuse lasts. And Allah Knows Best.

I have been married for five years. My husband has two sons from his first marriage. Nevertheless, I took care of his children, and gave birth to a baby boy who is now three years old. Unfortunately, we keep fighting all the time; sometimes over his two sons and sometimes over his family. If I serve his family members and praise them, he treats me kindly. If I don`t, he turns my life into living hell. What should I do?

All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions.

Spouses should live with each other on a footing of kindness and equity. In your case, constructive dialogue is the best course of action. We advise you to be patient, commit your affair to Allah and ask Him to help you. We also recommend that you seek the help of the people of goodness and make them fix things between you and your husband. If all attempts for reconciliation fail then go to court, but we remind you that a problem, which could be solved with a beautiful word, is no problem at all, so praise family and children and try your best to win their hearts. And Allah The Almighty Knows Best.

Which hour coincides with the last third of the night?

This hour could be figured out by calculating the number of night hours which start at sunset, and end at dawn break, then the total is divided on three to get the result.

Is a person who is in a state of Janabah (major ritual impurity due to having a marital intercourse, ejaculation, menstruation, and post-delivery impurities) sinful if he/she goes about his/her daily life activities in that state i.e. without making Ghusl (ritual bath)?

It goes without saying that a Muslim should always be in a state of ritual purity so as to be able to perform prayers and recite Quran. It is from Sunnah (Prophetic tradition) that a Muslim hastens to make Ghusl from Janabah, but he/she is not sinful in case he/she delayed that provided that he/she doesn`t miss prayers. However, it is permissible for him/her to go about their daily activities while in a state of Janabah, but had better bathe in order not to miss any prayer.