Now after long and windy road updating the BIOS of this PC, I can see that the tendency of freezing has not disappeared.
If I leave the PC unattended after starting it, so that it stays showing login dialog, after some time it does not anymore respond. Today just a moment it stopped responding in the middle of writing this story.
I gathered two sets of logs, first containing journal0 and journal1, I think.
The second only journal0 after the latest or second latest freeze. Cannot pay attention precisely because there are so many of these freezes again. The files are 7zip files.
So, it seems the BIOS update to year 2014 version did not much help. I feel very worried when connecting somewhere involving payments… it may easily fail completely if this PC freezes.
Thanks for all the help!