Is it permissible for an engineer who supplies needs to factories to agree with an employee inside the factory to give him new orders in exchange for a percentage of the profit, and what is the ruling if that was at the employee's request, and what should he do if that has happened previously?

Looking into the worker's task: If it is by authorization from the factory and the factory approves what he writes, then it is not permissible to pay a commission to the worker, because what he does is a duty for which he receives a salary, and what he takes is a forbidden bribe. This could lead to favoritism towards you at the expense of the factory's needs. However, if his work only guides you to the factory's needs, then it is permissible to pay him a commission outside his official working hours, and the commission should be a fixed amount, not a percentage of the profit, due to uncertainty.