What should a person, who doubts the validity of his Wudu, or over performs it, do?
One who doubts the validity of his/her Wudu while performing it should redo it until he/she is certain of having attained purity. But, if doubt was after having performed Wudu, then he/she should not pay attention to that as doubt after the end of an act of worship does not count. This is of course in case doubt was within the reasonable limits since once it goes beyond that, it becomes a whispering of the Shaytaan (devil) which he/she should ignore as the Wudu is valid.
What is the ruling on someone who prays Fajr late, after sunrise, knowing that they wake up on time but return to sleep and do not perform it within its time?
It is obligatory to perform the prayer within its prescribed time. If someone wakes up and knows how to act, they must perform it before the time ends. If they delay it, they are sinful and must make it up. And Allah Knows Best.
Is it permissible to pray with a heater (stove) in front of me?
There is no harm in praying with a heater in front of you, as long as you do not intend to venerate the fire or imitate those who worship it. And Allah Knows Best.
I took a housing loan from the bank for a 20-year period. Four years have passed, and I recently learned that this loan is usurious. I wish to perform Umrah. Am I permitted to perform it? If not, what should I do?
You are permitted to perform Umrah. Strive to repay the debt in hopes of reducing the amount of usurious interest. Allah Says (What means): "And there are others who have acknowledged their sins. They had mixed a righteous deed with another that was bad. Perhaps Allah will turn to them in forgiveness. Indeed, Allah is Forgiving and Merciful." [At-Tawbah/102]. And Allah Knows Best.