The way DL translates this sentence, "...broils sausage" is treating "sausage" as a generic term, so whenever Keoki cooks sausage, he habitually broils it. Given ka, It could also say that he broils THE sausage. Either interpretation should be correct. Itʻs a bit ambiguous.
I agree, "Keoki broils the sausage" sounds more natural to me! I think all the variations you suggested should be accepted. :D And, even though it sounds a little odd, I could see using "Keoki broils sausage" if i wanted to specify how Keoki usually cooks sausage, in general.
Well, I suppose I would’ve thought it would be: “Keoki broils THE sausage” since “Keoki broils sausage” didn’t sound quite right to me. He either broils “A” sausage, or “THE” sausage if it’s just a single sausage. Or if plural, “Keoki broils sausageS” would sound right. Just not “Keoki broils SAUSAGE.” But I wasn’t sure if I was wrong about the English on this one or not since I put “Keoki broils the sausage” and got it wrong. But I thought there was a chance that I could be wrong, so I figured I’d ask and see if anyone else thought differently than I did.
The English sentence sounds more like a habitual statement. It's like me saying, "I walk to work." I'm not necessarily walking to work now, but I have in the past and I'm likely to in the future.
Hawaiian seems to use definite articles a lot more than English, but the English translations don't always reflect the same amount of definiteness. If there's some particular subtlety or absence of it that isn't easily conveyed in a translation, it would helpful if the course creators would explain in the grammar notes.