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 it permissible to move a grave from its current location to another place, for example, from a garden in a home to a cemetery, knowing that the grave has been there for a long time, about fifty years?

It is not permissible to move the deceased from his grave, as this may result in breaking his bones and violating his sanctity. Such actions are not allowed. And Allah Knows Best.

Is the patient who is on dialysis twice a week obliged to observe fasting? Is his fasting on the days he is on dialysis considered valid or not?

Praise be to Allah the Lord of the Worlds.

Dialysis invalidates fasting because of the nutritional fluid used in that procedure, as pointed by specialized doctors, in addition to causing bodies to enter the stomach. Therefore, it is recommended that the patient who had undergone dialysis to observe fasting for the rest of that day, if he is able to, and make up for it after Ramadan. However, if the doctor told him that fasting, at any time, would damage his health, then he must break his fast and pay a ransom against every missed day. We pray that Allah blesses this person with recovery. And Allah The Almighty Knows Best.

What is the ruling on not offering prayer in a nearby mosque, and going to a distant one?