Må is used to show whether someone feels good or bad, and it cannot describe emotions. Känna sig is used to show emotions more specific than words that mean "good" or "bad." Here are some examples: Jag mår dåligt (I feel good/well.) or Jag mår fantastiskt! (I feel fantastic). Må is usually used with bra, dåligt, or words that mean basically the same thing (such as fantastiskt). Here are some more examples: Jag känner mig trött (I feel tired) or Jag känner mig glad (I feel happy). So, long story short, use må to say whether you feel good or bad, and use känna sig to say how you feel in a way that is more related to your emotions or not meaning good/bad.
It's also worth noting I believe må can be used by medical professionals, when you go see your doctor they might say "hur mår du" and they're asking what's wrong with you (i.e. what brought you to see the doctor). Just thought I'd throw that in for some extra information about må :)
Open https://www.duolingo.com in a browser. Click on a lesson. Click on the lightbulb icon that pops out of the lesson. It'll take you to something like this: https://www.duolingo.com/skill/sv/Verbs%3A-Modal/tips-and-notes
känner sig is reflexive, it is about the feeling a person has, what someone feels like in
Jag känner mig glad – 'I feel happy' (I am experiencing this feeling)
känns is used for describing how something feels to someone else. Rummet känns kallt - 'The room feels cold' – it's not the room that experiences the feeling.
This is a deponent verb, read more about them here: https://www.duolingo.com/comment/6094592
I'm guessing it's the passive voice. It's not literally asking how "it" feels, it's asking how is it felt. For instance, let's say you're trying on a pair of shoes, and someone asks, "How do they feel?" The shoes aren't doing the feeling; the shoes are being felt. So it's really like they're asking, "How do you feel (with the shoes on)?"
Does that make sense? Of course, I could be wrong, but this is my guess. Confirmation from someone who knows would be good.