A desert isn't defined by its sand and the Gobi Desert is primarily, if not entirely, temperate but you wouldn't think twice about calling it a desert. I think the question is fine as is.
The giveaway is that the Sahara is "second" meaning they are counting things which aren't usually considered deserts, aka Antarctica. Sahara is traditionally the largest desert.
For the Bikini Atoll question, I tried bombs, nukes, nuclear weapons, nuclear warfare, and many other variations of the same idea. Instead of adding more type-ins, I recommend that you rewrite the question to get a more specific answer.
In Shakespeare's Julius Caesar, his last words are actually this complete sentence: "Et tu Brute? Then fall Caesar!". The second part means Caesar understands that his death is unavoidable if even Brutus has betrayed him.
I always confuse Chopin and Liszt. Quizmaster, could you use a similar question to the last one in an upcoming “hard knowledge quiz”? It could be: “Which artist’s full initials were PDJFdPJNMdlRCdlSTRyP?”
Hydrogen bomb? Thermonuclear weapon/bomb? All these should be included as answers.