Can books and papers that contain the name of Allah be placed next to pillows that were ritually impure then dried and are now covered with a clean cover, and what is the ruling on purifying those pillows?

The dryness of an impurity does not purify it. Placing books and papers containing the remembrance of Allah next to something impure is not unlawful, as long as it does not touch the impurity. However, it is better to keep them away from proximity to impurities, out of reverence for the شعائر الله (sacred rites/symbols of Allah). If the pillow has a pure cover, then there is no harm in placing books on it. Impure pillows are purified by washing them until the impurity is removed.