Are the profits from a project established with usurious loan financing unlawful to spend on the family, and what is the status of the office if spending from it is unlawful, knowing that I have started repaying the loan and am currently unable to repay it in full?

Borrowing with interest is explicit usury (riba). The borrower must repent and seek forgiveness. If it is possible to return the money without an increase, then it is not permissible to pay the interest. Similarly, if it is possible to convert the loan into a benevolent loan (qard hasan). Since you were unaware of the prohibition of usury, there is no sin upon you. There is no harm in benefiting from the project. You are not required to repay the amount in a single lump sum, unless they compel you to pay the interest, in which case it is better to get rid of the usury all at once.