Those paper masks do little if anything to help the wearer from taking in anything. They do not filter the air—they are far too porous and loose-fitting to filter. They do help prevent the wearer from spreading their germs and touching nose/mouth as you said, but they are not an effective air filtration device.
Yes, yes they do. I can find a million pictures of N95 masks that look just like a cheap little paper mask (not like surgical masks -- not rectangular. Just cheap and like it's made of paper similar to a paper filter).