Is it permissible to take a commission on the purchase of a computer for one of the employer's sons, or for tasks that are not part of my responsibilities in the employment contract, especially since I know that another employee did so and the manager did not object to it?

If the tasks assigned to you by your manager are outside the scope of your contract, you have the right to demand payment for them. If he refuses, then refuse to perform the work. It is not permissible to take compensation for this work secretly, because it is ghulul (embezzlement), and Allah Almighty says: "And whoever embezzles, will bring forth on the Day of Resurrection that which he embezzled. Then every soul will be recompensed for what it earned, and they will not be wronged."