On the English side, the Cambridge Dictionary entry (https://dictionary.cambridge.org/dictionary/english/something) for "something" notes the following: "Something" is not usually used in negatives and questions AND "Anything" is usually used instead of "something" in negative sentences and questions. This sentence is both a question and a negative, and something is not currently accepted. "Why doesn't he have ANYTHING to eat or drink," however, is.
We just had a phrase where "nemá" was translated as "there is nobody" (Now there is nobody to take care of their bear), and it refused to accept "now they have nobody to take care of their bear". Is that nema different from this nema (maybe no long á on the end)? Or is there another reason why I can't translate this one as: Why isn't there anything to eat or drink? I tried and it wasn't accepted. But it seems to me as though it's the same construction as the bear one. Just wondering... Thanks.
It is a bit different, yes. The other one with the bear is a bit special usage, please see the discussion there. Notice the subordinate clause there. Report missing or unclear translations there.
This one here is quite ordinary mít=to have which can also be used with an infinitive.