I already accept that I have bad sleep patterns and not worry about it, but still I get "brain-fog" most of the days and perform poorly. Wish to know how solve that!

Have you tried getting more sleep? ;]

I sleep erratically but is common to sleep 12 hours!

That is often very much part of it, yes. And knowing that a bad night paradoxically makes it harder to sleep next night sure doesn't help.

But I can also have sleepless nights where I manage not to think, just lie there and exist. More pleasant but I can't say it makes any difference next day.

Just as you can be wildly off in your estimate of how much you slept during a night you can be wildly off in your estimation of your own alertness and mental state. You can be wrong about how you feel, for much the same reason placebos work or people are suggestible; we don’t actually have a privileged window into our own minds, we’re observers too.

I agree. I've tried to keep a detailed log of my sleep, including how I felt next morning and throughout the day and to my frustration I never figured out how to even remotely reliable measure sleep/rest.

Is sleeping 8 hours better than sleeping 4 hours? Depends...