Who is obligated to fast?

The one obligated to fast is the Muslim who is of sound mind, mature, capable of fasting, and free from obstacles such as menstruation or postpartum bleeding. And Allah Knows Best.

Sometimes I receive a message containing a picture of someone desecrating the Noble Quran. The sender asks recipients to send that message to their contacts as an act of defending the Quran. What should I do when receiving such messages?

Praise be to Allah, the Lord of the Worlds.

You don`t have to circulate that message, because this isn`t the proper way to defend the Quran. And Allah The Almighty Knows Best.

Is it permissible for the mother to offer an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)for her son?

Aqeeqah is due on the one obliged to provide for the newborn, and it is permissible for the grandfather, or the mother to offer the Aqeeqah.

How should a person who is afflicted with continued major ritual impurity (incontinence of urine, bleeding outside the monthly period) perform ablution?

Such a person should make ablution for every prayer after its due time and after removing impurities from their body and outfit, and should place a fresh diaper whenever needed so as for the impurity not to spread out. They should also perform prayer immediately even if incontinence of urine continued, and should repeat the aforementioned for every obligatory prayer, then perform optional prayer as much as they want.