Would "How does Corinna feel" work? (The owl rejected it). :( Edit - since that's how they used it in another sentence, they should add it to the accepted translations. I can't now because I just got it correct.
It's not really an inquiry into her feelings. Often we say things like: "quomodo res se habet?" or "omnia bene se habent", and they certainly do not mean "how does the situation feel?" and "everything feels good", at least in the emotional sense of the word "feeling".
No, no -- in American English (at least out here in California) when we ask how someone is feeling, it usually refers to their health. Of course we are lacking context here. If there had been a whole story about changes at Corinna's workplace and you asked, "How does Corinna feel about that?" it would obviously be asking her feelings about the new changes.
I similarly tried, "How is Corinna feeling?" and it didn't work. Seems like it's better English than "doing," so I'm a little confused.
I personally think there's a difference in the meaning. If I say "How are you?" (or also "how are you doing"?) it's a greeting, if I ask "How do you feel?" I'm trying to know if you have an headache or something. I don't think you would greet someone with "How are you feeling?", it sounds too clinical.
I agree that "How are you/is he (doing)" is more general than "How are you/is he feeling". I would only use "feeling" when I'm specifically inquiring about health.
"How are you (doing)?" -- A general inquiry that is often used as a standard greeting and therefore tends to have a standard (as opposed to a real, honest) response.
"How are you feeling?" -- I'm aware that you've been ill and I'm expressing real concern and expect a real, honest answer.
There is a significant difference in greetings in Standard American English and in British English, though. In Standard American English, "Are you all right?" is only used in response to witnessing someone have a mishap. Maybe they walked into a pole, maybe they can't seem to stop coughing. In AAVE and British English, however "[Are (you)] all right?" is just a standard informal greeting.