I prayed all the obligatory prayers in congregation, but after finishing the `Isha prayer, I remembered that I had forgotten to pray Dhuhr. What should I do, and is my prayer invalid?
Your prayers are valid, but you must make up the Dhuhr prayer as soon as you remember it, based on the saying of the Prophet (peace be upon him): "Whoever forgets a prayer must pray it as soon as they remember it; there is no expiation for it except this." [Muslim]. And Allah knows best
Is it permissible for a pious Muslim woman to stay with her husband who had quit praying out of laziness?
Quitting prayer is one of the major grave sins that come after disbelieving in Allah, but the wife of such a person isn`t considered divorced, rather, she should exert all her efforts in order to bring him back to the way of Islam. However, if his sin is likely to lure her from the way of Islam, then she had better separate from him by lawful means such as Mokhal`aa (When a wife pays a compensation for her husband in return for divorcing her). Moreover, if she exercises patience, and remains steadfast on her faith, then there is no harm in doing that.
After I had prayed, I found a drop of menstrual blood and was unsure when that happened; what is the ruling on my prayer and fast?
All praise is due to Allah, peace and blessing be upon the Messenger of Allah.
Your prayer and fast are correct ,and you should not make up for them, and we ask Allah, The Almighty, to duely reward you for these acts of worship. Your menses start once you see blood because the situation remains as such unless there is certainty or predominant conjecture, as per the Fiqh maxim: "Certainty is not removed by doubt". And Allah Knows Best.
I underwent a procedure for a molar pregnancy (hydatidiform mole), and after that, the bleeding continued for more than two months, during which I did not pray. Do I need to make up the missed prayers?
If you have previously experienced postpartum bleeding, the duration of the current bleeding is treated the same as your previous postpartum period. Any bleeding that exceeds this duration must be considered irregular bleeding (istihada), and you must make up the missed prayers. If this is the first time, then any bleeding beyond sixty days is considered irregular bleeding. You must perform ghusl, pray, and make up the prayers for the days beyond the sixty-day limit. And Allah Knows Best.