It's moments like this, I'm glad I knew some Punjabi, otherwise I don't think I would have guessed all the other variants of uncles, aunts and grandparents. This is the only one where I had to look, as the Punjabi version is maasar and maasi.
I hope someone updates the actual definitions to these words.
Is it common to omit possessives before family members (like maybe this could be translated "My uncle isn't ill" even though it's not word-for-word)?
Yes, I was thinking the same. I was marked incorrect for that reason, because I wrote "My uncle is not ill"
So many different words for uncle and aunt which shows how important family relationships are in Hindi culture.
Yes, it can get even more complicated with separate words even for dad's older brother and dad's younger brother! I'd like to note that, coloquially, mom's sister and mom's brother are not pronounced like they are here on duolingo. We say "maasee" rather than "mausee" and "maama" rather than "mausa." I've actually never heard them said the way duolingo says them.
I think the situation is similar in many other Asian languages. In Chinese, there are also many different words for relatives, even for siblings (older brother =/= younger brother, older sister =/= younger sister)