The sentence that requires translation is "Το παγωτό είναι γλυκό." It includes the direct article. Therefore, it's referencing a specific ice cream. The answer should also include the direct article. Because it's a word-select question/puzzle translation without the article as an option to select, it's incorrect.
Technically, dessert is "επιδόρπιο". Sweets can be eaten as dessert, but you wouldn't call a healthier dessert (for example fruits with yogurt) "γλυκό". So, they shouldn't be used interchangeably, even though "επιδόρπιο" isn't used as much, and - let's face it - we most probably are going to choose a sweet for dessert! :)
Pudding is completely different if we're referring to the AE use. It's a sweet made from cornflour, milk sugar etc and served at room temperature or refrigerated. Ice cream is of course frozen. "Pudding" is also a BE expression used for dessert in general. I think there would need to be a different wording here to accept this as a dessert. In other sentences, we use "dessert/sweet/pudding" interchanageably.
Trying to explain pronunciation can be tricky even in Greek where most letters are straight forward as they appear. It just happens the the letter "Γγ" is a bit tricky. So, to just go here where you can hear it pronounced by native Greek speakers. But no you would not pronounce this without the "g".
Why is "γ" sometimes pronounced like a "g" and sometimes like a "y"? Is there any rule?
γ is pronounced [ɣ] before a back vowel [a o u] and is pronounced [ʝ] before a front vowel [e i].
γκ is pronounced [ɡ] or [ŋɡ] in more or less free variation.
γγ is always pronounced [ŋɡ].