I forgot one other probable/possible clue:

Yesterday, when turning on the water in my newly installed sink and it
was draining, I heard a distinct glug_glug_glug from from the toilet! I
never heard that before. I had to leave, and I was thinking it over. I
remembered that the sink had drained slowly for a day or two in the
summer but then seemed alright, so I figured maybe I had a trapped air
problem in the sink drain that was causing it to drain slowly. I thought
that maybe if I flushed the toilet, the sink would drain again OK. If
only my problem could be so easily solved. Of course, flushing the
toilet didn't help!

Dan

PS Yes, it's pretty obvious that fixing this one will be no easy fix.
At the very least, tearing open floor/wall and replacing bad drain pipes
and considerable repair to repair floor/wall. The whole house could use
a plumbing upgrade. I think I'm going to be soliciting quotes soon.
Thanks for the answers.