Am I the only one having plasma 5 (5.3.2 currently, but this has been going on for quite a while) crashing many times daily? Appears to happen when pressing ESC mostly in web browsers, but it is not possible for me to find a pattern. Anyone with similar experience?

you maybe want to check the backtrace ("developer information") and either google for the crashy line (or present it for inspection)

It is not possible to get it, I am trown back to the shell, after which the display manager starts (the new default qt one, forgot its name)

Either ksmserver crashes or the X11 server.
Xorg would usually write its backtrace into /var/log/Xorg.1.log (ie. the log of the last session, /var/log/Xorg.0.log is the current one)
For ksmserver, you'd likely have to move to another virtual terminal and gdb attach to it from there.

See eg. https://community.kde.org/KWin/Debugging - you only want to debug "ksmserver" rather than "kwin_x11"