What kind of wall do I have, and do I need anchors?

I have a 36"x60" 30 lbs frameless mirror that I want to hang up on my wall, but I can't seem to find the studs! I've tried using a magnetic stud finder with no luck. I've drilled multiple holes in my wall and here is what I found:

• There's an outlet at the bottom right edge of my wall. I drilled one hole at eye level about 9" to the left of that and did hit wood! I thought I found a stud, but then I drilled another hole closer to the floor where the base of the mirror would be. It's directly underneath the first hole but now there's no wood! I'm so confused.
• I drilled a bunch of holes elsewhere in the wall, but no wood. All of these holes are pretty deep, like 1 1/2". Is my wall not hollow?
• Shining a flashlight into some of these holes makes me think it's not made of drywall? Could it be concrete?
• Also, with every hole, I seem to have drilled through some sort of metal fence thing about 7/8" from the surface. Is there like a metal mesh inside my wall?

The surface of my wall is textured and I live in an old apartment in San Francisco (I have rent control so it was probably built before 1979).

I've given up looking for a stud and just use wall anchors instead, but it doesn't look like my wall is hollow so the anchors probably won't even come out the other side. What kind of wall do I have, and given the thickness, can I just use the screws by themselves to hang up the mirror?