It is looks like Parallels Tools was not installed properly. Your parallels-tools-install.log finished with:
2: /lib/modules/4.19.0-6-686-pae/build
3: /usr/lib/parallels-tools/kmods/prl_tg/Toolgate/Guest/Linux/prl_drm
Start checking drm core on kernel /lib/modules/4.19.0-6-686-pae/build...
But this means that only kernel space drivers was installed but user space and ddx drivers not installed.
Success Parallels Tools installation will be indicated by such content of parallels-tools-install.log at the bottom:
Perform initramfs update.
'/home/alexkod/cdrom0/installer/parallels_tools.initramfs-hook' -> '/usr/share/initramfs-tools/hooks/parallels_tools'
update-initramfs: Generating /boot/initrd.img-4.19.0-6-686-pae
Send installed Parallels Tools version to dispatcher.
>>> Postinstall
Writing OS version and Xorg version
Enabling PRL_GL
Starting prltoolsd service:
Parallels Guest Tools were installed successfully!
Please, reboot your OS to finish installation of Parallels Guest Tools.
You need to reinstall Parallels Tools:
1) Uninstall Parallels Tools first:
Connect Parallels Tools image "/Applications/Parallels Desktop.app/Contents//Resources/Tools/prl-tools-lin.iso" to VM.
Mount it inside VM if not automatically mounted.
Run /media/cdrom0/install -r
Reboot VM.
2) Install Parallels Tools as usually.