What should I do, as the bathroom doorknob became impure because of me, and I did not inform my father about it, and he might have prayed with impurity on his hand because of me?

If you are not certain about the impurity of the handle, then nothing is required of you, because the default state of things is purity, and a ruling of impurity is only made with certainty. Therefore, do not pay attention to doubts and whispers. However, if you are certain of the impurity, then you must inform whoever will use it, as an act of advice to them. If the hand touches the impurity and both are dry, then the impurity does not transfer. If the hand is wet and the impurity is dry, there is a difference of opinion regarding its transfer, and the default is that impurity does not transfer when there is doubt.