What should I do with the plaques bearing the name of Allah that were manufactured and charged by non-Muslims, and which I fear they may have handled disrespectfully? Should I hang them on the wall? And would I be sinful if my friends admire them and ask for similar ones?

There is no harm in seeking out plaques inscribed with the names of Allah Almighty, and it is permissible to hang them on walls as long as they are kept away from disrespect and are not placed in locations of immorality and transgression. The possibility of disrespect when moving them is not considered, nor is that regarded as aiding in what is forbidden.