Is it permissible to take a sum of money mixed with usurious interest to pay for the costs of a training course and medical treatment, knowing that one is in financial hardship and need?

There is no harm in taking the offered money, because the ruling on usurious interest is to dispose of it by giving it to the poor and the needy and spending it on general Muslim welfare. The owner of the money should be advised to repent and cease dealing with usurious banks, due to the danger this poses to his religion and his worldly life.