How do you know if a noun is feminine or masculine? Like for example, how would you know that billee is feminine without memorizing it?
If the noun ends in a long 'i' then it is probably feminine. Also if it refers to a female object., e.g. 'sister'. This is a peg for the memorizing process.
When hovering over "बड़ी" it says "old (living things)", so I answered "this cat is old" and got it wrong. Does this mean that it can mean "old" but not always?
Yes. बड़ी/बड़ा means old only in the context of humans. Examples -
मेरा भाई मुझसे बड़ा है। - My brother is older than me.
मेरे दो बड़े भाई हैं। - I have two elder brothers.
बड़ा/बड़ी can mean "big/large" in any context.
How do we let Duolingo know they are cutting off the upper loop on the words in the multiple choice section?