Is it permissible to pay a sum of money to retrieve a confiscated driver's license, especially if abandoning agricultural work due to the absence of the license would lead to significant losses, and is this amount considered a bribe? And if payment is permissible, is it permissible to take the paid amount from the father's account, which contains usurious increments?

If you have the right to reclaim the license, and its withholding is an injustice, then it is permissible to pay money to get it back. However, if you do not have a right to it, then it is not permissible, because it is a forbidden bribe. Bribes are of two types: a forbidden one by which one achieves falsehood, and a permissible one for someone who uses it to attain their legitimate right or to دفع an injustice. Your father must dispose of the usurious gains by spending them on the poor and on the welfare of Muslims. It is not permissible for him to give them to you to ward off injustice if you are not poor.