neder comes from ned (down) and del means part. It basically means "the downward part (of your clothes)". Something you put on to cover your nether regions, basically. In German, you can say "Unterteil" which is constructed the same way (unter = down/under & Teil = part); if you'd use that in a clothes context, it can describe anything from a skirt to pants.
?@ BorgPrincess: Maybe you would - I wouldn't. ;-)
Wiktionary does not have an entry on "Unterteil" and the entry on "Oberteil" only mentions "Unterteil" as the opposite of the meaning not related to clothes. Duden has an entry on "Unterteil", but it does not mention any relation to clothes, whereas its entry on "Oberteil" does.
I'm not stating said use of "Unterteil" is wrong, but I'd like to point out it's not universal. :-)
True, but a lot of them start out as boys or start out as girls identified by others as boys (different trans women look back on their childhood in different ways), and many of those children will have wanted to wear skirts and been forbidden to. So I'm not surprised that Michaela, as a trans woman, likes the idea of a boy wearing a skirt, even though she is not a boy (wearing a skirt or otherwise) herself.
It is "technically" /neðɐdelə/ which should mean "naytha dayluh" more or less but the IPA doesn't really have a good symbol for Danish soft D, so they just cheap out and use a ð. If you say naythadayluh people will know what you're talking about but you'll sound funny and people will almost certainly ask you to say "rød grød med fløde" in which every word has a soft D.
A Danish soft D is more like saying an L with the tongue on the bottom teeth instead of the top ones.
I would say the literal translation sounds a little weird to some people and so they translate it as is wearing in stead. I don't know this for sure, but maybe Danish doesn't have a word for wear as in to wear clothes and so this is duolingo way of getting that across. Just a guess though. Feel free to correct me in the comments if I got something wrong.