"Although he doesn't like to talk, he likes to smile."
I don't really know but my dictionary says
笑 = laugh, smile
微笑 = smile (and translates literally to "small laugh" so that makes sense)
So I guess it would be safe to use the first one to mean "laugh" and the second one to mean "smile" but I don't know what other more subtle distinctions in meaning are possible.
Yes, I think that's the basic distinction, but that (a) there's less of a clear line between them in Chinese, and (b) there are euphony effects (and nuances, as you say) to consider that native speakers will naturally have more of a feel for.
As far as I recall, a user called Mr.rM and I had a substantial discussion on this page, but all of his posts seem to have been deleted from Duolingo, and unfortunately that means several useful discussions we had in the Chinese forums are gone as well.
Apparently Duo thinks so because I got marked wrong for using it there. IRL there's not a thing wrong with it and in fact it makes the sentence less ambiguous.
So far in this particular lesson I have gotten six different questions wrong that Duo should have accepted. So glad I'm not paying money for this course.