Is the father a Mahram (Non-marriageable) to his son`s mother-in-law?
The father is a non-Mahram (Marriageable) to his son`s mother-in-law, so it is impermissible for them to look at each other, or to have a seclusion (Khalwah).
Is it permissible for a Muslim woman to wear trousers at home?
Wearing trousers at home isn't prohibited so long as non-Mahrams do not see her. And Allah Knows Best.
Is it permissible for a woman to offer the obligatory prayer after Adhaan (call for prayer), and before Iqamah (The announcement that the prayer is about to begin) in the mosque?
Yes, it is permissible for a woman to offer the obligatory prayer immediately after the Adhan and before the Iqamah in the mosque. And Allah Knows Best.
I had my menstrual period at the beginning of Ramadan for six days, then it ended and I became pure. After four days, I started noticing some blood again, which has lasted for two days now, but it is not as heavy as menstrual blood. Is this blood considered menstrual blood, and what is the ruling regarding my prayers, fasting, and reading the Quran during this period?
All praise is due to Allah, and peace and blessings be upon our Prophet Muhammad.
The minimum duration of menstruation is one day and one night, and its maximum is fifteen days. Any blood beyond this period is considered irregular bleeding (Istihada). Since the bleeding did not exceed fifteen days, it is considered menstrual blood within the regular cycle. Therefore, you should not pray or fast until the bleeding stops and the signs of purity appear. If the bleeding stops before fifteen days from when it first started, then all the blood you saw is considered menstrual blood, and you must make up the fasts, but not the prayers. If it exceeds fifteen days, then the first six days are menstrual blood, and the blood that follows is considered irregular bleeding. Your prayers and fasting are valid, and there is no issue with them. And Allah Knows Best."
*This answer was updated on [18/5/2023].