Is my prayer considered invalid if I prostrated on the seven limbs, but my knees were not directly on the prayer rug due to a notebook being between them and the rug?

Your prayer is valid even if there is a notebook between your knees and the ground, because what matters is the stability of the limb. If there is a barrier between it and the ground, it does not harm, for the notebook does not prevent your knee from being stable. Similarly, prayer is valid on a barrier such as wool, hair, or fur, or on something that prevents the hardness of the ground, like a padded mattress, or on what the earth produces, as long as the prostration is stable.