"He is not well."
Translation:Ihm ist nicht gut.
So, we get dative, and not dative examples to do; and it still seems confusing to me. But, based on that it is, for me, in the Dative section, I'm to learn that even if Duo doesn't express it using 'him' in English, we're to recognize only that it's Dative because that's the section. I probably encountered this, and got it wrong in earlier levels, and I did often just give up and give Duo what it wants... I'll try to remember that it's possible to express this with ihm in a Dative sentence. That seems the easiest course of action. I hope we'll get more examples.
AFAIK, it's "Ihm fühlt sich nicht wohl." since it's dative, ... er is not dative, I believe. Oh hand on, ... it's only a dative if the thingymajig requires it, ... so I've been told, ... soooo, .... I've never seen fühlen used in a dative, in that way, if at all, so maybe it's right? In any case, might be worth reporting, to get the mods/admins to check it over.
"Er" is the Nominative case, so it can be used as the subject of "Er ist krank." but this expression has a hidden "it" for the subject "Es", and "ihm" is the indirect object. "It goes badly for him." is "Es geht ihm schlecht." or "Ihm geht es schlecht.", so this expression is "Ihm ist schlecht." and is similarly constructed, but they don't bother to put the subject "es". These are two really common ways to say "He is sick." or "He is ill."
"wichtig" means "important". "richtig" means "correct or right" https://dictionary.reverso.net/german-english/wichtig https://dictionary.reverso.net/german-english/richtig
I see this as one of those expressions regarding subjective feeling (bad) vs objectively (bad). Examples would be. Mir geht es schlecht., or the famous Uns ist warm. I'm thinking that Ihm geht es nicht gut. or Ihm geht es schlecht. would work; but couldn't try it out.
About using Er, I think you'll find the best explanation, unless someone knows one better, can be found at the "Uns ist warm" post where the same question was raised about why "Uns" and not "Wir" which I think is the answer for why "Ihm" and not "Er". That's located here: Uns ist warm. The post ultimately says it has to do with being Dative but goes into extended correct information (German language structure in expressions) as well as people's confusion over it... including mine. lol