Is it permissible to slaughter one animal as a sacrifice and an Aqeeqah (the sheep slaughtered on the seventh day from the child`s birth)?
It is impermissible to do so since each of them is slaughtered for a different reason.
Is it permissible for a mother to stop her daughter from marrying a respectable, God-fearing young man because he isn't college/university graduate?
It is impermissible to deny a woman her right in getting married except for a lawful reason, and problems can be solved through dialogue. However, she can file a suit in order for the judge to have a say in that regard.
Is a person rewarded for refraining from all that breaks their fast when required to do so, and is it considered a valid fast?
If a person eats or drinks thinking that Fajr has not yet arrived, but then someone informs them that Fajr had already begun, they must refrain from eating for the rest of the day and make up the fast later.
If they observe the required restraint (imsak), they will be rewarded for obeying the command because fulfilling an obligation brings reward.
However, this is not considered a valid fast in terms of rulings. For example:
● It is not disliked (makruh) for them to use a miswak after noon.
● They are not encouraged to hasten the breaking of the fast at sunset.
● Other fasting-related rulings do not apply to them.
Is the prayer of a woman who is led by an Imam via T.V. permissible?
All perfect praise be to Allah, The Lord of The Worlds, and may His Peace and Blessings be upon our Prophet Muhammad and upon all of his family and companions. Amongst the conditions for the validity of prayer is that both the Imam and those led by him must be in the same place. Thus, the prayer of the person who is being led by a televised Imam is invalid unless he/she was with him in the same mosque. And Allah Knows Best.