"Are you busy?"
Does Duolingo actually "teach" anything? As long as you can tap the word to see the translation, then I don't see what it would matter.
You can't if it's multiple choice (which is what this one was for me).
I think it was expecting elimination of known words (assuming you had choices)
So, DuoLingo, you should ask people if they are free in Japan. Asking if they are busy is weird. Use お暇ですか?
I'm hearing いそましい. Is the が softer and i just can't hear well, or is duo mispronouncing this word?
Nasalization. The pronunciation of several things on this course are different from in the areas I lived.
...Same way you pronounce any other Japanese が? The consonant sound is often slightly nasalized, but otherwise it's pretty straightforward.