I have layer property manager anchored to the left side of my screen. Where are the layer controls. e.g. "New Layer" control?
It seems you have some unusual issues with your AutoCAD. I would review your system specs as compared to the recommended system requirements, and also the other software you have running in the background.
I get this sometimes to. I think its probably memory as if I close Autocad then re-open the icons are there.
It happens (or seems to) if I have been in & out of a lot of different drawings. Now if it does I take it as "warning" that the software might crash & that I might loose work so do a close & re-open.
Not ideal but has saved some heartache. Yes I do have automatic save on but sometimes you can do a lot in a couple of mins.
While you wait to get that resolved, you can use the -layer command at the command line.