Is it permissible to take a loan from the bank to cover the costs of equipment for a government youth project, while refusing to take the portion allocated for personal expenses, knowing that the bank is a partner in the project?

There is no harm in taking installments from the bank if no usurious interest is taken on them. Otherwise, it is forbidden to take them. There is no difference between installments as long as the bank gives money and takes more than it gave.