Unable to hang things in certain walls
Your walls ,because of the year you stated it was built are probably plaster. Plaster walls use lathing as an attachment under the plaster , but I don't see this as the problem you are encountering when securing accessories to the wall. I'm thinking that while drilling the wall in the bathroom: 1) you may have encountered a cast vent/waste pipe beneath the wall or 2) it could be a pipe or electrical wire protective plate that are installed when a wire or pipe are installed through a wall stud. Either of these would explain not being able to drill an opening. The first thing to be sure of is the material of the walls. Try to drill a small opening in an unobtrusive location ( down low and in a closet). You should see grainy course sand ejected as the bit pierces the wall.