Help identify wall & how to hang things on it
Your wall looks like plaster.  It is most likely laid over wood lath, metal mesh or backing board.
Sometimes you can bang very thin sharp nails into plaster successfully.  But yours seems to be more brittle by your description.
Try drilling through the plaster with a small sharp drill bit in a few places.    Feel when the plaster transitions to something else.  Then clean the drill bit and keep drilling, looking at the shavings to determine what your backing is.  If it's wood lath you may happen to drill between laths, that's why I say &quot;in a few places&quot;.  You could also drill a half-inch hole and buy a cheap endoscope to see definitively what's behind the wall.    (Edit: Some say you should use a masonry bit.  I get better results with a sharp wood bit but you should experiment to find what's best on your walls.   And for the initial experimentation I describe above, the ideal thing is a hand drill.   And there is an additional possibility I should describe: the plaster may be over brick in some places, eg over a chimney.  In that case you should use appropriate methods for brick.)
If it's metal or backing board you can use plastic anchors for plaster (don't use drywall anchors) or toggles depending on what you're hanging.  If it's wood lath my preferred technique is to drill just up to the wood, then drill a small pilot hole through the lath, put a shortened plastic anchor into the hole (it will only go up to the lath) and then use a 2-1/2&quot; screw.  The anchor will do some of the work and the lath will help a great deal.  The combination is quite strong.
I also second the advice in the other answer about using the picture rail as intended.   If your picture rail is an ACTUAL picture rail (it's hard to tell from the photo) it will have a rounded top designed for special picture rail hooks.  Buy them.  Then don't need ANY tools or fasteners at all!