I also would love to have an "official" answer to this question.
My translation -- I don't TAKE CARE OF František -- was accepted. Given that the correct translation shown above is "I DO NOT CARE ABOUT František," it would seem that both emotional and physical "caring" are covered (so to speak).
But I also wonder whether "I DO NOT CARE FOR" (as in, "I don't like") František" would also work.
I don't know about the Russian ся, but what it is curious in the Czech se, compared to the same thing in the Romance language (and also in the Germanic ones, except English), is that "se" stays the same in all the different forms of the verb. I mean, in Spanish you say "yo me preocupo", "tú te preocupas", "ella se preocupa", etc. In German you say "Ich fühle mich", "Du fühlst dich", and so on, but in Czech is always "se". That's interesting.
Question: does this verb mean "care about" when it comes to humans and "take care of" when it comes to animals, or is the rule not so hard and fast? Like is there a different verb that means "take care of" a person if, say, that person is your child or sick or otherwise needs caring for?
You can complain at the lamp office of the main train station. Or at https://support.duolingo.com/hc/en-us/articles/204728264-How-do-I-report-a-bug-
But not here, please.