Is a woman's prayer performed while following an Imam whose prayer is being broadcasted via the television valid, and does she receive the reward of congregational prayer?

Is it permissible for a guardian (Big brother) to unlawfully stop his sister from getting married?

If the guardian denies her right in getting married for an unlawful reason, she should go to court in order to settle that matter, and the guardian is considered sinful in this case.

Is Zakah (obligatory charity) due on the Zakah money received by a poor person, and reached a Nissab (minimum amount liable for Zakah), and a whole lunar year had lapsed over having it in his possession?

Yes, the poor who possessed a Nissab for a whole lunar year is obliged to pay the Zakah due on that money even if it was given to him as a Zakah money in the first place. And Allah Knows Best.

What is the ruling on the fasting of a woman who has reached menopause if menstrual blood flows?

If a woman reaches the age of menopause (which is usually sixty-two) and her menses have ceased, then she sees blood after that, and its duration is not less than a day and a night (24 hours), it is menstruation (hayd). If it is less than a day and a night, she is considered as having non-menstrual vaginal bleeding (mustahada), so she fasts and prays. However, she must perform ablution for every obligatory prayer after its time enters, pray immediately, and be treated as a person with a continuous condition. There is no specific end limit for a woman's menstruation; it is possible as long as the woman is alive. And Allah the Almighty knows best.