What is the ruling on an employee changing their start date to benefit from an additional salary, then employing their brother to work in their stead for that salary, and is it permissible to take money from the state and spend it on those in need?

If the manager is authorized to account for the days mentioned for your friend, then there is no harm for your friend in benefiting from the payment. Otherwise, it is not permissible for him to benefit from it, and he must return it to the employer. It is not sufficient for him to give it to another person to work with for the benefit of the entity, unless the entity agrees. Nor is it sufficient for him to spend it on the needy as long as he is able to deliver it to the rightful owner.

As for taking state money without a just cause, it is not permissible, even with the intention of spending it on the needy; because the end does not justify the means, and Allah is good and accepts only what is good.