In my area, we receive many weekly newspapers and flyers who’s majority content consists of ads or news, but also a dvar torah. 1. Can this be brought in a bathroom? 2. Can I throw the paper in the trash, or put in a seperate plastic bag beofre throwing out? 3. What about papers that are strewn outside?
If you know that the flyers have a regular Dvar Torah, they must be treated with respect, meaning that they should not be brought into the bathroom, and not be thrown away. Of course, this applies only to the page on which the Dvar Torah appears, and after this page is cut out, the rest can be discarded.
Sources: Although the status of printed material is a matter of doubt among authorities, poskim are stringent concerning newspapers with a regular Dvar Torah, and obligate their handling with respect. See Chazon Ish, YD 164:3; Yerushas Hapleitah 29; Minchas Yitzchak 1:17; Achiezer 3:32; Shevet Halevi 5:162.