Is it permissible to deposit the actual amount into the bank and utilize its interest to pay off an alleged debt—which is much greater than the original amount—and was not actually received?

What your friend did is an injustice, and it is not permissible for him to take anything in excess of his right, even if a judge ruled it, because a judge's ruling does not make the unlawful lawful. The Prophet, peace and blessings be upon him, said: "If I rule for someone a portion of his brother's right, he should not take it, for I am only cutting off for him a piece of fire."

Depositing money in banks with usury is a major sin, and it is not permissible to undertake this to pay off a debt or a fine or anything else, except in cases of necessity.

Necessity permits forbidden things, but scholars differed on whether this includes usury. Even according to the view that permits it due to necessity, it is not permissible to undertake it except under certain conditions, the most important of which is that the necessity cannot be averted except through this forbidden act. You must first search for permissible means, such as mediating to reduce the amount or to pay it in installments, or taking a permissible loan, or investing money in a permissible investment, or selling properties that can be dispensed with. As long as there are legitimate alternatives, this is not considered a case of necessity that permits dealing with forbidden usury.