Is it obligatory to dispose of papers that contain the names of Allah, and would I be sinful if I did not do so? And would I be sinful for discarding papers that do not contain any of the names of Allah?

Arabic letters must be respected when shredding, burning, or burying papers containing them in a pure place, or collecting them for later disposal. It is not permissible to use them as wrappers, dining mats, or to throw them in the trash.