Is it permissible to step or sit on impurities (urine, feces, or ordinary filth) while holding a paper with the name of Allah on it, or having it in one's pocket?

If the intent is to sit on impure places outside the restroom while having something inscribed with the name of Allah in one’s hand or pocket, there is no harm in that. However, if the intent is to touch impurity inside the restroom, scholars have explicitly stated that it is disliked to enter the restroom with anything inscribed with the name of Allah.