Is it permissible to swear by (Allah "The Living")?
Yes, it is permissible because "The Living" is one of Allah`s Attributes.
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].
Does passing wind from the anus affect ritual purity?
Ablution is nullified by the passing of wind from the anus, but washing the anus is not required as wind leaves no impurity.
During Ramadan, a man had sexual intercourse with his wife. What is the expiation for that? And is he permitted to pay the expiation?
If a man has intercourse with his wife during the daytime in Ramadan, he must make up for that day and offer expiation. The expiation is fasting for two consecutive months. If he is unable to do so, he must feed sixty needy people. And Allah Knows Best.